How neuronal spike trains encode external information is a hot topic in neurodynamics studies. In this paper, we investigate the dynamical states of the Hodgkin-Huxley neuron under periodic forcing. Depending on the p...How neuronal spike trains encode external information is a hot topic in neurodynamics studies. In this paper, we investigate the dynamical states of the Hodgkin-Huxley neuron under periodic forcing. Depending on the parameters of the stimulus, the neuron exhibits periodic, quasiperiodic and chaotic spike trains. In order to analyze these spike trains quantitatively, we use the phase return map to describe the dynamical behavior on a one-dimensional （1D） map. According to the monotonicity or discontinuous point of the 1D map, the spike trains are transformed into symbolic sequences by implementing a coarse-grained algorithm -- symbolic dynamics. Based on the ordering rules of symbolic dynamics, the parameters of the external stimulus can be measured in high resolution with finite length symbolic sequences. A reasonable explanation for why the nervous system can discriminate or cognize the small change of the external signals in a short time is also presented.展开更多
A novel approach to the inverse problem of diffusively coupled map lattices is systematically investigated by utilizing the symbolic vector dynamics. The relationship between the performance of initial condition estim...A novel approach to the inverse problem of diffusively coupled map lattices is systematically investigated by utilizing the symbolic vector dynamics. The relationship between the performance of initial condition estimation and the structural feature of dynamical system is proved theoretically. It is found that any point in a spatiotemporal coupled system is not necessary to converge to its initial value with respect to sufficient backward iteration, which is directly relevant to the coupling strength and local mapping function. When the convergence is met, the error bound in estimating the initial condition is proposed in a noiseless environment, which is determined by the dimension of attractors and metric entropy of the system. Simulation results further confirm the theoretic analysis, and prove that the presented method provides the important theory and experimental results for better analysing and characterizing the spatiotemporal complex behaviours in an actual system.展开更多
Based on symbolic dynamics, a novel computationally efficient algorithm is proposed to estimate the unknown initial vectors of globally coupled map lattices （CMLs）. It is proved that not all inverse chaotic mapping ...Based on symbolic dynamics, a novel computationally efficient algorithm is proposed to estimate the unknown initial vectors of globally coupled map lattices （CMLs）. It is proved that not all inverse chaotic mapping functions are satisfied for contraction mapping. It is found that the values in phase space do not always converge on their initial values with respect to sufficient backward iteration of the symbolic vectors in terms of global convergence or divergence （CD）. Both CD property and the coupling strength are directly related to the mapping function of the existing CML. Furthermore, the CD properties of Logistic, Bernoulli, and Tent chaotic mapping functions are investigated and compared. Various simulation results and the performances of the initial vector estimation with different signal-to- noise ratios （SNRs） are also provided to confirm the proposed algorithm. Finally, based on the spatiotemporal chaotic characteristics of the CML, the conditions of estimating the initial vectors usiug symbolic dynamics are discussed. The presented method provides both theoretical and experimental results for better understanding and characterizing the behaviours of spatiotemporal chaotic systems.展开更多
The symbolic dynamics of a Belykh-type map （a two-dimensional discon- tinuous piecewise linear map） is investigated. The admissibility condition for symbol sequences named the pruning front conjecture is proved unde...The symbolic dynamics of a Belykh-type map （a two-dimensional discon- tinuous piecewise linear map） is investigated. The admissibility condition for symbol sequences named the pruning front conjecture is proved under a hyperbolicity condition. Using this result, a symbolic dynamics model of the map is constructed according to its pruning front and primary pruned region. Moreover, the boundary of the parameter region in which the map is chaotic of a horseshoe type is given.展开更多
A novel computationally efficient algorithm in terms of the time-varying symbolic dynamic method is proposed to estimate the unknown initial conditions of coupled map lattices （CMLs）. The presented method combines s...A novel computationally efficient algorithm in terms of the time-varying symbolic dynamic method is proposed to estimate the unknown initial conditions of coupled map lattices （CMLs）. The presented method combines symbolic dynamics with time-varying control parameters to develop a time-varying scheme for estimating the initial condition of multi-dimensional spatiotemporal chaotic signals. The performances of the presented time-varying estimator in both noiseless and noisy environments are analysed and compared with the common time-invariant estimator. Simulations are carried out and the obtained results show that the proposed method provides an efficient estimation of the initial condition of each lattice in the coupled system. The algorithm cannot yield an asymptotically unbiased estimation due to the effect of the coupling term, but the estimation with the time-varying algorithm is closer to the Cramer-Rao lower bound （CRLB） than that with the time-invariant estimation method, especially at high signal-to-noise ratios （SNRs）.展开更多
In this paper, we discuss a class of piecewise linear hyperbolic maps on the 2-torus. These maps arise in the second-order digital fdter with two＇ s complement arithmetic. By introducing codings underlying the map op...In this paper, we discuss a class of piecewise linear hyperbolic maps on the 2-torus. These maps arise in the second-order digital fdter with two＇ s complement arithmetic. By introducing codings underlying the map operations, we give some admissibility conditions for symbolic sequences and find some periodic properties of these symbolic sequences. Then we use these conditions to check the admissibility of periodic symbol sequences.展开更多
This paper is contributed to the combinatorial properties of the MSS sequences, which are the periodic kneading words of quadratic maps defined on a interval. An explicit expression of adjacency relations on MSS seque...This paper is contributed to the combinatorial properties of the MSS sequences, which are the periodic kneading words of quadratic maps defined on a interval. An explicit expression of adjacency relations on MSS sequences of given lengths is established.展开更多
This paper is contributed to the combinatorial properties of the periodic kneading words of antisymmetric cubic maps defined on a interval. The least words of given lengths, the adjacency relations on the words of giv...This paper is contributed to the combinatorial properties of the periodic kneading words of antisymmetric cubic maps defined on a interval. The least words of given lengths, the adjacency relations on the words of given lengths and the parity-alternative property in some sets of such words are established.展开更多
Utilizing the character of chaos, the sensitivity to the initial conditions, the concept and the structure of so-called chaotic transducer based on Tent map is provided in this paper creatively. The possibility of app...Utilizing the character of chaos, the sensitivity to the initial conditions, the concept and the structure of so-called chaotic transducer based on Tent map is provided in this paper creatively. The possibility of applying the basic theory of symbolic dynamics to the measurement is presented and proved. Then, the theoretical model of chaotic transducer is realized by using the switched capacitor and the basic experimental results are given. The transducer has such characters as high sensitivity, resolution, the simple structure and combining signal amplification with A/D. The new area of the application of chaos is exploited. Meanwhile, it provides a new method of exploring the structure of new type transducer.展开更多
The authors consider the billiard system with finitely many convex scatters with smooth boundary satisfying the visibility assumption on the plane and prove that the closed orbits for the billiard flow is uniformly di...The authors consider the billiard system with finitely many convex scatters with smooth boundary satisfying the visibility assumption on the plane and prove that the closed orbits for the billiard flow is uniformly distributed.展开更多
We systematically investigate the periodic orbits of the Lorenz flow up to certain topological length. As an alternative to Poincar6 section map analysis, we propose a new approach for establishing one-dimensional sym...We systematically investigate the periodic orbits of the Lorenz flow up to certain topological length. As an alternative to Poincar6 section map analysis, we propose a new approach for establishing one-dimensional symbolic dynamics based on the topological structure of the orbit. A newly designed variational method is stable numerically for cycle searching, and two orbital fragments can be used as basic building blocks for initialization. The topological classification based on the entire orbital structure is revealed to be effective. The deformation of periodic orbits with the change of parameters provides a chart to the periods of cycles. The current research may provide a methodology for finding and systematically classifying periodic orbits in other similar chaotic flows.展开更多
Based on forbidden patterns in symbolic dynamics, symbolic subsequences are classified and relations between forbidden patterns, correlation dimensions and complexity measures are studied. A complexity measure approac...Based on forbidden patterns in symbolic dynamics, symbolic subsequences are classified and relations between forbidden patterns, correlation dimensions and complexity measures are studied. A complexity measure approach is proposed in order to separate deterministic （usually chaotic） series from random ones and measure the complexities of different dynamic systems. The complexity is related to the correlation dimensions, and the algorithm is simple and suitable for time series with noise. In the paper, the complexity measure method is used to study dynamic systems of the Logistic map and the Henon map with multi-parameters.展开更多
Let T：X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f：X → R^d is a Hlder continuous function with ∫_X^（fdm） = 0.If the components of f are cohomologously i...Let T：X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f：X → R^d is a Hlder continuous function with ∫_X^（fdm） = 0.If the components of f are cohomologously independent, then there exists a positive definite symmetric matrix σ~2：=σ~2 （f ） such that S^fn √ n converges in distribution with respect to m to a Gaussian random variable with expectation 0 and covariance matrix σ~2 . Moreover, there exists a real number A 〉 0 such that, for any integer n ≥ 1,Π（ m＊（ 1√ nS f n ）,N （0,σ~2 ） ≤A√n, where m＊（1√ n S^fn）denotes the distribution of 1√ n S^fn with respect to m, and Π is the Prokhorov metric.展开更多
We are concerned with the sets of quasi generic points in finite symbolic space. We estimate the sizes of the sets by the Billingsley dimension defined by Gibbs measures. A dimension formula of such set is given, whic...We are concerned with the sets of quasi generic points in finite symbolic space. We estimate the sizes of the sets by the Billingsley dimension defined by Gibbs measures. A dimension formula of such set is given, which generalizes Bowen＇s result. An application is given to the level sets of Birkhoff average.展开更多
Many Internet-GIS have been implemented on the web and they are increasingly becoming an important part of multimedia cartography that has much more users as compared to traditional GIS production media.Internet GIS t...Many Internet-GIS have been implemented on the web and they are increasingly becoming an important part of multimedia cartography that has much more users as compared to traditional GIS production media.Internet GIS technology has provided the GIS dynamic information acquisition with technical support.Also,the visualization technology of electronic map has provided tools for GIS symbols with dynamic characteristics.On the basis of GIS dynamic information acquisition,the design idea and implementation methods of dynamic symbols in dynamic GIS are presented in this article.展开更多
Railway point machine(RPM)condition monitoring has attracted engineers’attention for safe train operation and accident prevention.To realize the fast and accurate fault diagnosis of RPMs,this paper proposes a method ...Railway point machine(RPM)condition monitoring has attracted engineers’attention for safe train operation and accident prevention.To realize the fast and accurate fault diagnosis of RPMs,this paper proposes a method based on entropy measurement and broad learning system(BLS).Firstly,the modified multi-scale symbolic dynamic entropy(MMSDE)module extracts dynamic characteristics from the collected acoustic signals as entropy features.Then,the fuzzy BLS takes the above entropy features as input to complete model training.Fuzzy BLS introduces the Takagi-Sug eno fuzzy system into BLS,which improves the model’s classification performance while considering computational speed.Experimental results indicate that the proposed method significantly reduces the running time while maintaining high accuracy.展开更多
The embedding of the Bernoulli shift into the logistic map x→μx（1 - x） for μ 〉 4 is reinterpreted by the theory of anti-integrability： it is inherited from the anti-integrable limit μ→∞.
In this paper, we consider a two-parameter family of systems E<sub>ε</sub> in which E<sub>0</sub> has a contour consisting of a saddle point and two hyperbolic periodic orbits, i.e., the situa...In this paper, we consider a two-parameter family of systems E<sub>ε</sub> in which E<sub>0</sub> has a contour consisting of a saddle point and two hyperbolic periodic orbits, i.e., the situation is similar to that described by the Lorenz equations for parameters b=8/3, σ=10, r=r<sub>1</sub>≈24.06. For the generic unfolding E<sub>ε</sub>of E<sub>0</sub>, we find three kinds of infinitely many bifurcation curves and establish the correspondence of the trajectories which stay forever in a sufficiently small neighborhood of the contour with symbolic systems of finite or countably infinite symbols; these results can be used to explain the turbulence behaviors appearing at the critical value r=r<sub>1</sub>≈24.06 observed on computer for Lorenz equations in a precise mathematical way.展开更多
In this paper, the authors first construct a dynamical system which is strongly mixing but has no weak specification property. Then the authors introduce two new concepts which are called the quasi-weak specification ...In this paper, the authors first construct a dynamical system which is strongly mixing but has no weak specification property. Then the authors introduce two new concepts which are called the quasi-weak specification property and the semi-weak specification property in this paper, respectively, and the authors prove the equivalence of quasi-weak specification property, semi-weak specification property and strongly mixing.展开更多
In this paper, we construct a special class of subshifts of finite type. By studying the spectral radius of the transfer matrix associated with the subshift of finite type, we obtain an estimation of its topological e...In this paper, we construct a special class of subshifts of finite type. By studying the spectral radius of the transfer matrix associated with the subshift of finite type, we obtain an estimation of its topological entropy. Interestingly, we find that the topological entropy of this class of subshifts of finite type converges monotonically to log（n ＋ 1） （a constant only depends on the structure of the transfer matrices） as the increasing of the order of the transfer matrices.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.60871085)the Natural Science Foundation of Zhejiang Province,China (Grant No.Y1100119)
文摘How neuronal spike trains encode external information is a hot topic in neurodynamics studies. In this paper, we investigate the dynamical states of the Hodgkin-Huxley neuron under periodic forcing. Depending on the parameters of the stimulus, the neuron exhibits periodic, quasiperiodic and chaotic spike trains. In order to analyze these spike trains quantitatively, we use the phase return map to describe the dynamical behavior on a one-dimensional （1D） map. According to the monotonicity or discontinuous point of the 1D map, the spike trains are transformed into symbolic sequences by implementing a coarse-grained algorithm -- symbolic dynamics. Based on the ordering rules of symbolic dynamics, the parameters of the external stimulus can be measured in high resolution with finite length symbolic sequences. A reasonable explanation for why the nervous system can discriminate or cognize the small change of the external signals in a short time is also presented.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60571066,60271023 and 61072037)the Natural Science Foundation of Guangdong Province,China (Grant No. 07008126)
文摘A novel approach to the inverse problem of diffusively coupled map lattices is systematically investigated by utilizing the symbolic vector dynamics. The relationship between the performance of initial condition estimation and the structural feature of dynamical system is proved theoretically. It is found that any point in a spatiotemporal coupled system is not necessary to converge to its initial value with respect to sufficient backward iteration, which is directly relevant to the coupling strength and local mapping function. When the convergence is met, the error bound in estimating the initial condition is proposed in a noiseless environment, which is determined by the dimension of attractors and metric entropy of the system. Simulation results further confirm the theoretic analysis, and prove that the presented method provides the important theory and experimental results for better analysing and characterizing the spatiotemporal complex behaviours in an actual system.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61072037 and 60271023)the Natural Science Foundation of Guangdong Province,China (Grant No. 10151503101000011)
文摘Based on symbolic dynamics, a novel computationally efficient algorithm is proposed to estimate the unknown initial vectors of globally coupled map lattices （CMLs）. It is proved that not all inverse chaotic mapping functions are satisfied for contraction mapping. It is found that the values in phase space do not always converge on their initial values with respect to sufficient backward iteration of the symbolic vectors in terms of global convergence or divergence （CD）. Both CD property and the coupling strength are directly related to the mapping function of the existing CML. Furthermore, the CD properties of Logistic, Bernoulli, and Tent chaotic mapping functions are investigated and compared. Various simulation results and the performances of the initial vector estimation with different signal-to- noise ratios （SNRs） are also provided to confirm the proposed algorithm. Finally, based on the spatiotemporal chaotic characteristics of the CML, the conditions of estimating the initial vectors usiug symbolic dynamics are discussed. The presented method provides both theoretical and experimental results for better understanding and characterizing the behaviours of spatiotemporal chaotic systems.
基金Project supported by the National Natural Science Foundation of China(Nos.11172246 and 11572263)
文摘The symbolic dynamics of a Belykh-type map （a two-dimensional discon- tinuous piecewise linear map） is investigated. The admissibility condition for symbol sequences named the pruning front conjecture is proved under a hyperbolicity condition. Using this result, a symbolic dynamics model of the map is constructed according to its pruning front and primary pruned region. Moreover, the boundary of the parameter region in which the map is chaotic of a horseshoe type is given.
基金supported by the National Natural Science Foundation of China(Grant Nos 60271023 and 60571066)the Natural Science Foundation of Guangdong Province,China(Grant Nos 5008317 and 7118382)
文摘A novel computationally efficient algorithm in terms of the time-varying symbolic dynamic method is proposed to estimate the unknown initial conditions of coupled map lattices （CMLs）. The presented method combines symbolic dynamics with time-varying control parameters to develop a time-varying scheme for estimating the initial condition of multi-dimensional spatiotemporal chaotic signals. The performances of the presented time-varying estimator in both noiseless and noisy environments are analysed and compared with the common time-invariant estimator. Simulations are carried out and the obtained results show that the proposed method provides an efficient estimation of the initial condition of each lattice in the coupled system. The algorithm cannot yield an asymptotically unbiased estimation due to the effect of the coupling term, but the estimation with the time-varying algorithm is closer to the Cramer-Rao lower bound （CRLB） than that with the time-invariant estimation method, especially at high signal-to-noise ratios （SNRs）.
基金Project supported by National Natural Science Foundation of Chi-na (Grant No .10471087) ,and Shanghai Municipal Commission ofEducation (Grant No .03AK33)
文摘In this paper, we discuss a class of piecewise linear hyperbolic maps on the 2-torus. These maps arise in the second-order digital fdter with two＇ s complement arithmetic. By introducing codings underlying the map operations, we give some admissibility conditions for symbolic sequences and find some periodic properties of these symbolic sequences. Then we use these conditions to check the admissibility of periodic symbol sequences.
基金the National Natural Science Foundation of China (Grant No.10731040)
文摘This paper is contributed to the combinatorial properties of the MSS sequences, which are the periodic kneading words of quadratic maps defined on a interval. An explicit expression of adjacency relations on MSS sequences of given lengths is established.
基金the National Natural Science Foundation of China (Grant No.10731040)
文摘This paper is contributed to the combinatorial properties of the periodic kneading words of antisymmetric cubic maps defined on a interval. The least words of given lengths, the adjacency relations on the words of given lengths and the parity-alternative property in some sets of such words are established.
文摘Utilizing the character of chaos, the sensitivity to the initial conditions, the concept and the structure of so-called chaotic transducer based on Tent map is provided in this paper creatively. The possibility of applying the basic theory of symbolic dynamics to the measurement is presented and proved. Then, the theoretical model of chaotic transducer is realized by using the switched capacitor and the basic experimental results are given. The transducer has such characters as high sensitivity, resolution, the simple structure and combining signal amplification with A/D. The new area of the application of chaos is exploited. Meanwhile, it provides a new method of exploring the structure of new type transducer.
基金This work is supported by the National Natural Science Foundation of China(10571174)
文摘The authors consider the billiard system with finitely many convex scatters with smooth boundary satisfying the visibility assumption on the plane and prove that the closed orbits for the billiard flow is uniformly distributed.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11647085,11647086,and 11747106)the Applied Basic Research Foundation of Shanxi Province,China(Grant No.201701D121011)the Natural Science Research Fund of North University of China(Grant No.XJJ2016036)
文摘We systematically investigate the periodic orbits of the Lorenz flow up to certain topological length. As an alternative to Poincar6 section map analysis, we propose a new approach for establishing one-dimensional symbolic dynamics based on the topological structure of the orbit. A newly designed variational method is stable numerically for cycle searching, and two orbital fragments can be used as basic building blocks for initialization. The topological classification based on the entire orbital structure is revealed to be effective. The deformation of periodic orbits with the change of parameters provides a chart to the periods of cycles. The current research may provide a methodology for finding and systematically classifying periodic orbits in other similar chaotic flows.
基金Project supported by the National Natural Science Foundation of China (Grant No.10871168)
文摘Based on forbidden patterns in symbolic dynamics, symbolic subsequences are classified and relations between forbidden patterns, correlation dimensions and complexity measures are studied. A complexity measure approach is proposed in order to separate deterministic （usually chaotic） series from random ones and measure the complexities of different dynamic systems. The complexity is related to the correlation dimensions, and the algorithm is simple and suitable for time series with noise. In the paper, the complexity measure method is used to study dynamic systems of the Logistic map and the Henon map with multi-parameters.
基金supported by the National Natural Science Foundation of China(10571174)the Scientific Research Foundation of Ministry of Education for Returned Overseas Chinese ScholarsScientific Research Foundation of Ministry of Human Resources and Social Security for Returned Overseas Chinese Scholars
文摘Let T：X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f：X → R^d is a Hlder continuous function with ∫_X^（fdm） = 0.If the components of f are cohomologously independent, then there exists a positive definite symmetric matrix σ~2：=σ~2 （f ） such that S^fn √ n converges in distribution with respect to m to a Gaussian random variable with expectation 0 and covariance matrix σ~2 . Moreover, there exists a real number A 〉 0 such that, for any integer n ≥ 1,Π（ m＊（ 1√ nS f n ）,N （0,σ~2 ） ≤A√n, where m＊（1√ n S^fn）denotes the distribution of 1√ n S^fn with respect to m, and Π is the Prokhorov metric.
基金supported by Program Caiyuanpeisupported by NSFC(11171128,11271148)
文摘We are concerned with the sets of quasi generic points in finite symbolic space. We estimate the sizes of the sets by the Billingsley dimension defined by Gibbs measures. A dimension formula of such set is given, which generalizes Bowen＇s result. An application is given to the level sets of Birkhoff average.
文摘Many Internet-GIS have been implemented on the web and they are increasingly becoming an important part of multimedia cartography that has much more users as compared to traditional GIS production media.Internet GIS technology has provided the GIS dynamic information acquisition with technical support.Also,the visualization technology of electronic map has provided tools for GIS symbols with dynamic characteristics.On the basis of GIS dynamic information acquisition,the design idea and implementation methods of dynamic symbols in dynamic GIS are presented in this article.
基金supported in part by the Fundamental Research Funds for the Central Universities(Grant No.2021RC271)NSFC(Grants No.62120106011,52172323 and U22A2046).
文摘Railway point machine(RPM)condition monitoring has attracted engineers’attention for safe train operation and accident prevention.To realize the fast and accurate fault diagnosis of RPMs,this paper proposes a method based on entropy measurement and broad learning system(BLS).Firstly,the modified multi-scale symbolic dynamic entropy(MMSDE)module extracts dynamic characteristics from the collected acoustic signals as entropy features.Then,the fuzzy BLS takes the above entropy features as input to complete model training.Fuzzy BLS introduces the Takagi-Sug eno fuzzy system into BLS,which improves the model’s classification performance while considering computational speed.Experimental results indicate that the proposed method significantly reduces the running time while maintaining high accuracy.
文摘The embedding of the Bernoulli shift into the logistic map x→μx（1 - x） for μ 〉 4 is reinterpreted by the theory of anti-integrability： it is inherited from the anti-integrable limit μ→∞.
文摘In this paper, we consider a two-parameter family of systems E<sub>ε</sub> in which E<sub>0</sub> has a contour consisting of a saddle point and two hyperbolic periodic orbits, i.e., the situation is similar to that described by the Lorenz equations for parameters b=8/3, σ=10, r=r<sub>1</sub>≈24.06. For the generic unfolding E<sub>ε</sub>of E<sub>0</sub>, we find three kinds of infinitely many bifurcation curves and establish the correspondence of the trajectories which stay forever in a sufficiently small neighborhood of the contour with symbolic systems of finite or countably infinite symbols; these results can be used to explain the turbulence behaviors appearing at the critical value r=r<sub>1</sub>≈24.06 observed on computer for Lorenz equations in a precise mathematical way.
基金supported by the National Natural Science Foundation of China(Nos.11261039,11661054)the Jiangxi Provincial Natural Science Foundation of China(No.20132BAB201009)the Visiting Scholar Special Funds of Development Program for Middle-aged and Young Teachers in Ordinary Undergraduate Colleges and Universities of Jiangxi Province
文摘In this paper, the authors first construct a dynamical system which is strongly mixing but has no weak specification property. Then the authors introduce two new concepts which are called the quasi-weak specification property and the semi-weak specification property in this paper, respectively, and the authors prove the equivalence of quasi-weak specification property, semi-weak specification property and strongly mixing.
基金Supported by National Science Foundation of China(Grant No.11371346)
文摘In this paper, we construct a special class of subshifts of finite type. By studying the spectral radius of the transfer matrix associated with the subshift of finite type, we obtain an estimation of its topological entropy. Interestingly, we find that the topological entropy of this class of subshifts of finite type converges monotonically to log（n ＋ 1） （a constant only depends on the structure of the transfer matrices） as the increasing of the order of the transfer matrices.
