本文研究了Hanski et al(1991)提出的生态学模型dx/dt=r0x(1-x/k)-cxy/d+x-gx2/(h2+x2);dy/dt=s0y(1-qy/x)。对捕食者既有HollingⅡ型功能性反应,又有HollingⅢ型功能性反应,对食饵来说既有广食者又有专食者,本文将分析Hanski et al(19...本文研究了Hanski et al(1991)提出的生态学模型dx/dt=r0x(1-x/k)-cxy/d+x-gx2/(h2+x2);dy/dt=s0y(1-qy/x)。对捕食者既有HollingⅡ型功能性反应,又有HollingⅢ型功能性反应,对食饵来说既有广食者又有专食者,本文将分析Hanski et al(1991)提出的模型的平衡点、极限环和全局渐近稳定性等动力学行为。展开更多
Complex dynamics of modified Hastings-Powell （HP） model （phytoplankton-zoo- plankton-fish） with Holling type IV functional response and density-dependent morta- lity （closure terms） for top predator species is i...Complex dynamics of modified Hastings-Powell （HP） model （phytoplankton-zoo- plankton-fish） with Holling type IV functional response and density-dependent morta- lity （closure terms） for top predator species is investigated in this paper. Closure terms describe the mortality of top predator in plankton food chain models. Modified HP model with Holling type IV functional response gives rise to similar type of chaotic dynamics （inverted ＂teacup attractor＂） as observed in original HP model with Holling type II functional response. It is observed that introduction of nonlinear closure terms eliminate chaos and system dynamics becomes stable. Observation of this paper support the ＂Steele-Henderson conjecture＂ that, nonlinear closure terms eliminate or reduces limit cycles and chaos in plankton food chain models. Chaotic or stable dynamics are numerically verified by Lyapunov exponents （LE） method and Sil＇nikov eigenvalue anal- ysis and also illustrated graphically by plotting bifurcation diagrams. It is assumed that mortality of fish population, caused by higher-order predators （which are not explicitly included in the model） is not constant, rather it exhibits random variation through- out the year. To incorporate the effect of random mortality of fish population, white noise term is introduced into the original deterministic model. It is observed that the corresponding stochastic model is stable in mean square when the intensity of noise is small. Keywords： Holling type IV; chaos; closure term; white noise; mean square stability展开更多
文摘本文研究了Hanski et al(1991)提出的生态学模型dx/dt=r0x(1-x/k)-cxy/d+x-gx2/(h2+x2);dy/dt=s0y(1-qy/x)。对捕食者既有HollingⅡ型功能性反应,又有HollingⅢ型功能性反应,对食饵来说既有广食者又有专食者,本文将分析Hanski et al(1991)提出的模型的平衡点、极限环和全局渐近稳定性等动力学行为。
文摘Complex dynamics of modified Hastings-Powell （HP） model （phytoplankton-zoo- plankton-fish） with Holling type IV functional response and density-dependent morta- lity （closure terms） for top predator species is investigated in this paper. Closure terms describe the mortality of top predator in plankton food chain models. Modified HP model with Holling type IV functional response gives rise to similar type of chaotic dynamics （inverted ＂teacup attractor＂） as observed in original HP model with Holling type II functional response. It is observed that introduction of nonlinear closure terms eliminate chaos and system dynamics becomes stable. Observation of this paper support the ＂Steele-Henderson conjecture＂ that, nonlinear closure terms eliminate or reduces limit cycles and chaos in plankton food chain models. Chaotic or stable dynamics are numerically verified by Lyapunov exponents （LE） method and Sil＇nikov eigenvalue anal- ysis and also illustrated graphically by plotting bifurcation diagrams. It is assumed that mortality of fish population, caused by higher-order predators （which are not explicitly included in the model） is not constant, rather it exhibits random variation through- out the year. To incorporate the effect of random mortality of fish population, white noise term is introduced into the original deterministic model. It is observed that the corresponding stochastic model is stable in mean square when the intensity of noise is small. Keywords： Holling type IV; chaos; closure term; white noise; mean square stability
