The oscillation behavior of a two-dimension lattice-gas Brusselator model was investigated. We have adopted a coarse-grained kinetic Monte Carlo （CG-KMC） procedure, where m×m microscopic lattice sites are group...The oscillation behavior of a two-dimension lattice-gas Brusselator model was investigated. We have adopted a coarse-grained kinetic Monte Carlo （CG-KMC） procedure, where m×m microscopic lattice sites are grouped together to form a CG cell, upon which CG processes take place with well-defined CG rates. Such a CG approach almost fails if the CG rates are obtained by a simple local mean field （s-LMF） approximation, due to the ignorance of correlation among adjcent cells resulting fl＇om the trimolecular reaction in this nonlinear system. By proper incorporating such boundary effects, thus introduce the so-cMled b-LMF CG approach. Extensive numerical simulations demonstrate that the b-LMF method can reproduce the oscillation behavior of the system quite well, given that the diffusion constant is not too small. In addition, the deviation from the KMC results reaches a nearly zero minimum level at an intermediate cell size, which lies in between the effective diffusion length and the minimal size required to sustain a well-defined temporal oscillation.展开更多
We have studied the nucleation process of a two-dimensional kinetic Ising model subject to a bias oscillating external field, focusing on how the nucleation time depends on the oscillation frequency. It is found that ...We have studied the nucleation process of a two-dimensional kinetic Ising model subject to a bias oscillating external field, focusing on how the nucleation time depends on the oscillation frequency. It is found that the nucleation time shows a clear-cut minimum with the variation of oscillation frequency, wherein the average size of the critical nuclei is the smallest, indicating that an oscillating external field with an optimal frequency can be much more favorable to the nucleation process than a constant field. We have also investigated the effect of the initial phase of the external field, which helps to illustrate the occurrence of such an interesting finding.展开更多
Non-linear dynamics,fractals,periodic oscillations,bifurcations,chaos,and other terminologies have been used to describe human biological systems in the literature for a few decades.The eight manuscripts included in t...Non-linear dynamics,fractals,periodic oscillations,bifurcations,chaos,and other terminologies have been used to describe human biological systems in the literature for a few decades.The eight manuscripts included in this special issue discussed the historical background,展开更多
We have studied why PA （post-annealing） takes a long time to restore damaged crystallinity, which corresponds to repeat 10 10 times of lattice vibrations. Using a MD （molecular dynamics） simulation, we monitored t...We have studied why PA （post-annealing） takes a long time to restore damaged crystallinity, which corresponds to repeat 10 10 times of lattice vibrations. Using a MD （molecular dynamics） simulation, we monitored the time-series of the LRO （long-range order） parameter as LRO pattern, in the case of a type IIa diamond, from the beginning of ion impact by a sub-keV N2 beam implantation to a few nanoseconds, i.e., close to the feasible time limit for MD simulations. Due to the ion impact, the LRO parameter changed gradually from ＂LRO = 1＂ （crystal） to ＂LRO = 0＂ （amorphous）, showing the so-called critical slowing-down phenomenon. However, since PA was started the LRO pattern was not unique. The LRO patterns were grouped into more than three types of phases and the transition between them was also found. From the viewpoint of statistical dynamics, such chaotic variations in the LRO pattern may present that the system is a GCM （globally coupled map） of a complex system in a closed system. A GCM composed of coupled oscillators develops slowly to exhibit several different phases or ‘chaotic itinerancy＇ over time. Therefore, the long duration required for PA may be attributable to the nature of a complex system.展开更多
The heat distributions in the upper layers of the ocean have been studied and some important low frequency oscillations （LFOs） are already found and quantified by using various characteristic factors. In this paper,...The heat distributions in the upper layers of the ocean have been studied and some important low frequency oscillations （LFOs） are already found and quantified by using various characteristic factors. In this paper, the ‘heat center＇ of a sea area is defined with a simple method. Then the temperature data set of the upper layer of the global ocean （from surface down to 400 m, 1955-2003） is analyzed to detect the possible LFOs. Not only some zonal LFOs, which were reported early, but also some strong LFOs of the vertical and meridional heat distribution, which might imply some physical sense, are detected. It should be noted that the similar vertical oscillation pattern can be found in the Pacific Ocean, Atlantic Ocean and Indian Ocean. Results from some preliminary studies show that the vertical LFO might be caused by the solar irradiance anomalies. This study may help reveal some unknown dynamical processes in the global oceans and may also benefit other related studies.展开更多
In recent years,significant progress has been made regarding theories of intraseasonal oscillations (ISOs) (also known as the Madden-Julian oscillation (MJO) in the tropics).This short review introduces the latest adv...In recent years,significant progress has been made regarding theories of intraseasonal oscillations (ISOs) (also known as the Madden-Julian oscillation (MJO) in the tropics).This short review introduces the latest advances in ISO theories with an emphasis particularly on theoretical paradigms involving nonlinear dynamics in the following aspects:(1) the basic ideas and limitations of the previous and current theories and hypotheses regarding the MJO,(2) the new multi-scale theory of the MJO based on the intraseasonal planetary equatorial synoptic dynamics (IPESD) framework,and (3) nonlinear dynamics of ISOs in the extratropics based on the resonant triads of Rossby-Haurwitz waves.展开更多
The purpose of thepresent study is to determine whether a long range correlation is present in BZ （Belousov-Zhabotinskii） reaction and how this correlation varies with the change in concentration of the solution. To...The purpose of thepresent study is to determine whether a long range correlation is present in BZ （Belousov-Zhabotinskii） reaction and how this correlation varies with the change in concentration of the solution. To explore the dynamics of the system with change in concentration, phase space plot and power spectrum are studied. Hurst exponent is estimated using log log plot and R/S technique. We discuss the results which uncover how the system changes from an excitable steady stateto a limit cycle,展开更多
In order to explain the oscillation heat transfer dynamics of closed loop oscillation heat pipe (CLOHP) with two liquid slugs,analysis on the forces and heat transfer process of the partial gas-liquid phase system inv...In order to explain the oscillation heat transfer dynamics of closed loop oscillation heat pipe (CLOHP) with two liquid slugs,analysis on the forces and heat transfer process of the partial gas-liquid phase system involving multiple parameters was carried out,and a new type oscillation heat transfer dynamic model of the CLOHP was set up based on conservation laws of mass,momentum and energy.Application results indicate that its oscillation heat transfer dynamics features depend largely on the filling rate,pipe diameter and difference in temperature.Besides,oscillation intensity and transfer performance can be improved to a large extent by increasing the temperature difference properly and enlarging the pipe diameter within a certain range under a certain filling rate.展开更多
Background:Many disease-specific factors such as muscular weakness,increased muscle stiffness,varying postural strategies,and changes in postural reflexes have been shown to lead to postural instability and fall risk ...Background:Many disease-specific factors such as muscular weakness,increased muscle stiffness,varying postural strategies,and changes in postural reflexes have been shown to lead to postural instability and fall risk in people with Parkinson's disease(PD).Recently,analytical techniques,inspired by the dynamical systems perspective on movement control and coordination,have been used to examine the mechanisms underlying the dynamics of postural declines and the emergence of postural instabilities in people with PD.Methods:A wavelet-based technique was used to identify limit cycle oscillations(LCOs) in the anterior–posterior(AP) postural sway of people with mild PD(n = 10) compared to age-matched controls(n = 10).Participants stood on a foam and on a rigid surface while completing a dual task(speaking).Results:There was no significant difference in the root mean square of center of pressure between groups.Three out of 10 participants with PD demonstrated LCOs on the foam surface,while none in the control group demonstrated LCOs.An inverted pendulum model of bipedal stance was used to demonstrate that LCOs occur due to disease-specific changes associated with PD:time-delay and neuromuscular feedback gain.Conclusion:Overall,the LCO analysis and mathematical model appear to capture the subtle postural instabilities associated with mild PD.In addition,these findings provide insights into the mechanisms that lead to the emergence of unstable posture in patients with PD.展开更多
A dynamic model to describe the torsional vibration behaviors of a spur gear system is presented in this paper.Differential equations of nonlinear dynamics for the gear system exhibiting combined nonlinearity influenc...A dynamic model to describe the torsional vibration behaviors of a spur gear system is presented in this paper.Differential equations of nonlinear dynamics for the gear system exhibiting combined nonlinearity influence such as time-varying mesh stiffness,backlash and dynamic transmission error(DTE) were obtained.The method of multiple scales was employed to solve the nonlinear differential equations with parametric excitation in gear systems,by which both the frequency-response curves of the primary resonance caused by internal excitation and the analytical periodic solutions of nonlinear differential equations were obtained.The nonlinear influence of stiffness variation,the damping and the internal excitation on the system response was shown by frequency-response curves.Compared with numerical examples,the approximate analytical solutions are in good agreement with exact solutions,which proves that the method of multiple scales is effective for solving nonlinear problems in gear systems.展开更多
Based on Chua’s chaotic oscillation circuit, a fifth-order chaotic circuit with two memristors is designed and its corresponding dimensionless mathematic model is established. By using conventional dynamical analysis...Based on Chua’s chaotic oscillation circuit, a fifth-order chaotic circuit with two memristors is designed and its corresponding dimensionless mathematic model is established. By using conventional dynamical analysis methods, stability analysis of the equilibrium set of the circuit is performed, the distribution of stable and unstable regions corresponding to the memristor initial states is achieved, and the complex dynamical behaviors of the circuit depending on the circuit parameters and the memristor initial states are investigated. The theoretical analysis and numerical simulation results demonstrate that the proposed chaotic circuit with two memristors has an equilibrium set located on the plane constituted by the inner state variables of two memristors. The stability of the equilibrium set depends on both the circuit parameters and the initial states of the two memristors. Rich nonlinear dynamical phenomena, such as state transitions, transient hyperchaos and so on, are expected.展开更多
We consider the nonlinear functional dynamic equation （p（t）[（r（t）x^△（t））^△]γ）^△＋q（t）f（x（τ（t））） =0, for t≥t0,on a time scale T, where γ〉 0 is the quotient of odd positive integers, p, r, τ- ...We consider the nonlinear functional dynamic equation （p（t）[（r（t）x^△（t））^△]γ）^△＋q（t）f（x（τ（t））） =0, for t≥t0,on a time scale T, where γ〉 0 is the quotient of odd positive integers, p, r, τ- and q are positive rd-continuous functions defined on the time scale 1F, and lirut→∞ τ（t） = ∞. The main aim of this paper is to establish some new sufficient conditions which guarantee that the equation has oscillatory solutions or the solutions tend to zero as →∞ τ. The main investigation depends on the Riccati substitution and the analysis of the associated Riccati dynamic inequality. Our results extend, complement and improve some previously obtained ones. In particular, the results provided substantial improvement for those obtained by Yu and Wang [J Comput Appl Math, 225 （2009）, 531-540]. Some examples illustrating the main results are given.展开更多
By using some analytical techniques, modified inequalities and Mawhin＇s continuous theorem of coincidence degree theory, some simple sufficient conditions for the existence of at least one positive almost periodic so...By using some analytical techniques, modified inequalities and Mawhin＇s continuous theorem of coincidence degree theory, some simple sufficient conditions for the existence of at least one positive almost periodic solution of a generalized Mackey-Glass model of respiratory dynamics are obtained. Further, the globM attractivity of positive almost periodic solution of the above model is also studied. To the best of the author＇s knowl- edge, so far, the result of this paper is completely new. Finally, three examples are given to illustrate the main results in this paper.展开更多
文摘The oscillation behavior of a two-dimension lattice-gas Brusselator model was investigated. We have adopted a coarse-grained kinetic Monte Carlo （CG-KMC） procedure, where m×m microscopic lattice sites are grouped together to form a CG cell, upon which CG processes take place with well-defined CG rates. Such a CG approach almost fails if the CG rates are obtained by a simple local mean field （s-LMF） approximation, due to the ignorance of correlation among adjcent cells resulting fl＇om the trimolecular reaction in this nonlinear system. By proper incorporating such boundary effects, thus introduce the so-cMled b-LMF CG approach. Extensive numerical simulations demonstrate that the b-LMF method can reproduce the oscillation behavior of the system quite well, given that the diffusion constant is not too small. In addition, the deviation from the KMC results reaches a nearly zero minimum level at an intermediate cell size, which lies in between the effective diffusion length and the minimal size required to sustain a well-defined temporal oscillation.
基金V. ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China （No.21125313, No.20933006,and No.91027012）
文摘We have studied the nucleation process of a two-dimensional kinetic Ising model subject to a bias oscillating external field, focusing on how the nucleation time depends on the oscillation frequency. It is found that the nucleation time shows a clear-cut minimum with the variation of oscillation frequency, wherein the average size of the critical nuclei is the smallest, indicating that an oscillating external field with an optimal frequency can be much more favorable to the nucleation process than a constant field. We have also investigated the effect of the initial phase of the external field, which helps to illustrate the occurrence of such an interesting finding.
文摘Non-linear dynamics,fractals,periodic oscillations,bifurcations,chaos,and other terminologies have been used to describe human biological systems in the literature for a few decades.The eight manuscripts included in this special issue discussed the historical background,
文摘We have studied why PA （post-annealing） takes a long time to restore damaged crystallinity, which corresponds to repeat 10 10 times of lattice vibrations. Using a MD （molecular dynamics） simulation, we monitored the time-series of the LRO （long-range order） parameter as LRO pattern, in the case of a type IIa diamond, from the beginning of ion impact by a sub-keV N2 beam implantation to a few nanoseconds, i.e., close to the feasible time limit for MD simulations. Due to the ion impact, the LRO parameter changed gradually from ＂LRO = 1＂ （crystal） to ＂LRO = 0＂ （amorphous）, showing the so-called critical slowing-down phenomenon. However, since PA was started the LRO pattern was not unique. The LRO patterns were grouped into more than three types of phases and the transition between them was also found. From the viewpoint of statistical dynamics, such chaotic variations in the LRO pattern may present that the system is a GCM （globally coupled map） of a complex system in a closed system. A GCM composed of coupled oscillators develops slowly to exhibit several different phases or ‘chaotic itinerancy＇ over time. Therefore, the long duration required for PA may be attributable to the nature of a complex system.
文摘The heat distributions in the upper layers of the ocean have been studied and some important low frequency oscillations （LFOs） are already found and quantified by using various characteristic factors. In this paper, the ‘heat center＇ of a sea area is defined with a simple method. Then the temperature data set of the upper layer of the global ocean （from surface down to 400 m, 1955-2003） is analyzed to detect the possible LFOs. Not only some zonal LFOs, which were reported early, but also some strong LFOs of the vertical and meridional heat distribution, which might imply some physical sense, are detected. It should be noted that the similar vertical oscillation pattern can be found in the Pacific Ocean, Atlantic Ocean and Indian Ocean. Results from some preliminary studies show that the vertical LFO might be caused by the solar irradiance anomalies. This study may help reveal some unknown dynamical processes in the global oceans and may also benefit other related studies.
基金supported by the National Natural Science Foundation of China (Grant No. 40975028)
文摘In recent years,significant progress has been made regarding theories of intraseasonal oscillations (ISOs) (also known as the Madden-Julian oscillation (MJO) in the tropics).This short review introduces the latest advances in ISO theories with an emphasis particularly on theoretical paradigms involving nonlinear dynamics in the following aspects:(1) the basic ideas and limitations of the previous and current theories and hypotheses regarding the MJO,(2) the new multi-scale theory of the MJO based on the intraseasonal planetary equatorial synoptic dynamics (IPESD) framework,and (3) nonlinear dynamics of ISOs in the extratropics based on the resonant triads of Rossby-Haurwitz waves.
文摘The purpose of thepresent study is to determine whether a long range correlation is present in BZ （Belousov-Zhabotinskii） reaction and how this correlation varies with the change in concentration of the solution. To explore the dynamics of the system with change in concentration, phase space plot and power spectrum are studied. Hurst exponent is estimated using log log plot and R/S technique. We discuss the results which uncover how the system changes from an excitable steady stateto a limit cycle,
基金Project(531107040300)supported by the Fundamental Research Funds for the Central Universities in ChinaProject(51176045)supported by the National Natural Science Foundation of China
文摘In order to explain the oscillation heat transfer dynamics of closed loop oscillation heat pipe (CLOHP) with two liquid slugs,analysis on the forces and heat transfer process of the partial gas-liquid phase system involving multiple parameters was carried out,and a new type oscillation heat transfer dynamic model of the CLOHP was set up based on conservation laws of mass,momentum and energy.Application results indicate that its oscillation heat transfer dynamics features depend largely on the filling rate,pipe diameter and difference in temperature.Besides,oscillation intensity and transfer performance can be improved to a large extent by increasing the temperature difference properly and enlarging the pipe diameter within a certain range under a certain filling rate.
基金the National Science Foundation for partial financial support for this project provided through the grant CMMI-1300632Purdue University for partial financial support for this project through a Research Incentive Grant
文摘Background:Many disease-specific factors such as muscular weakness,increased muscle stiffness,varying postural strategies,and changes in postural reflexes have been shown to lead to postural instability and fall risk in people with Parkinson's disease(PD).Recently,analytical techniques,inspired by the dynamical systems perspective on movement control and coordination,have been used to examine the mechanisms underlying the dynamics of postural declines and the emergence of postural instabilities in people with PD.Methods:A wavelet-based technique was used to identify limit cycle oscillations(LCOs) in the anterior–posterior(AP) postural sway of people with mild PD(n = 10) compared to age-matched controls(n = 10).Participants stood on a foam and on a rigid surface while completing a dual task(speaking).Results:There was no significant difference in the root mean square of center of pressure between groups.Three out of 10 participants with PD demonstrated LCOs on the foam surface,while none in the control group demonstrated LCOs.An inverted pendulum model of bipedal stance was used to demonstrate that LCOs occur due to disease-specific changes associated with PD:time-delay and neuromuscular feedback gain.Conclusion:Overall,the LCO analysis and mathematical model appear to capture the subtle postural instabilities associated with mild PD.In addition,these findings provide insights into the mechanisms that lead to the emergence of unstable posture in patients with PD.
文摘A dynamic model to describe the torsional vibration behaviors of a spur gear system is presented in this paper.Differential equations of nonlinear dynamics for the gear system exhibiting combined nonlinearity influence such as time-varying mesh stiffness,backlash and dynamic transmission error(DTE) were obtained.The method of multiple scales was employed to solve the nonlinear differential equations with parametric excitation in gear systems,by which both the frequency-response curves of the primary resonance caused by internal excitation and the analytical periodic solutions of nonlinear differential equations were obtained.The nonlinear influence of stiffness variation,the damping and the internal excitation on the system response was shown by frequency-response curves.Compared with numerical examples,the approximate analytical solutions are in good agreement with exact solutions,which proves that the method of multiple scales is effective for solving nonlinear problems in gear systems.
基金supported by the National Natural Science Foundation of China (Grant No. 60971090)the Natural Science Foundations of Jiangsu Province, China (Grant No. BK2009105)
文摘Based on Chua’s chaotic oscillation circuit, a fifth-order chaotic circuit with two memristors is designed and its corresponding dimensionless mathematic model is established. By using conventional dynamical analysis methods, stability analysis of the equilibrium set of the circuit is performed, the distribution of stable and unstable regions corresponding to the memristor initial states is achieved, and the complex dynamical behaviors of the circuit depending on the circuit parameters and the memristor initial states are investigated. The theoretical analysis and numerical simulation results demonstrate that the proposed chaotic circuit with two memristors has an equilibrium set located on the plane constituted by the inner state variables of two memristors. The stability of the equilibrium set depends on both the circuit parameters and the initial states of the two memristors. Rich nonlinear dynamical phenomena, such as state transitions, transient hyperchaos and so on, are expected.
基金supported by King Saud University,Dean-ship of Scientific Research,College of Science Research Centre
文摘We consider the nonlinear functional dynamic equation （p（t）[（r（t）x^△（t））^△]γ）^△＋q（t）f（x（τ（t））） =0, for t≥t0,on a time scale T, where γ〉 0 is the quotient of odd positive integers, p, r, τ- and q are positive rd-continuous functions defined on the time scale 1F, and lirut→∞ τ（t） = ∞. The main aim of this paper is to establish some new sufficient conditions which guarantee that the equation has oscillatory solutions or the solutions tend to zero as →∞ τ. The main investigation depends on the Riccati substitution and the analysis of the associated Riccati dynamic inequality. Our results extend, complement and improve some previously obtained ones. In particular, the results provided substantial improvement for those obtained by Yu and Wang [J Comput Appl Math, 225 （2009）, 531-540]. Some examples illustrating the main results are given.
文摘By using some analytical techniques, modified inequalities and Mawhin＇s continuous theorem of coincidence degree theory, some simple sufficient conditions for the existence of at least one positive almost periodic solution of a generalized Mackey-Glass model of respiratory dynamics are obtained. Further, the globM attractivity of positive almost periodic solution of the above model is also studied. To the best of the author＇s knowl- edge, so far, the result of this paper is completely new. Finally, three examples are given to illustrate the main results in this paper.
