CHAOS BEHAVIOR IN THE DISCRETE BVP OSCILLATOR-Reference-Cited by-同舟云学术

CHAOS BEHAVIOR IN THE DISCRETE BVP OSCILLATOR

Published:2002-03 Issue:03 Volume:12 Page:619-627
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

JING ZHUJUN¹²,JIA ZHIYUAN³,WANG RUIQI³

Affiliation:

1. Department of Mathematics, Hunan Normal University, Changsha, 410081, Hunan Province, China

2. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China

3. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Beijing, 100080, China

Abstract

The discrete BVP oscillator obtained through the Euler method is investigated, and also first proved that there exist chaotic phenomena in the sense of Marotto's definition of chaos and two-period cycles. And numerical simulations not only show the consistence with the theoretical analysis but also exhibit the complex dynamical behaviors, including the ten-periodic orbit, a cascade of period-doubling bifurcation, quasiperiodic orbits and the chaotic orbits in Marotto's chaos and intermitten's chaos. The computations of Lyapunov exponents confirm the existence of dynamical behaviors.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127402004577

Reference14 articles.

1. Critical dynamics of the Bonhoeffer-van der Pol equation and its chaotic response to periodic stimulation

2. A mathematical model of periodic processes in membranes (with application to cell cycle regulation)

3. Impulses and Physiological States in Theoretical Models of Nerve Membrane

4. Unified mechanism for relay and oscillation of cyclic AMP in Dictyostelium discoideum.

5. A quantitative description of membrane current and its application to conduction and excitation in nerve

Cited by 20 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Bifurcation and Chaos of a Nonlinear Discrete-Time Predator-Prey Model Involving the Nonlinear Allee Effect;Discrete Dynamics in Nature and Society;2023-01-17

2. Two‐parameter bifurcation analysis of the discrete Lorenz model;Mathematical Methods in the Applied Sciences;2021-12-07

3. Extreme events in a forced BVP oscillator: Experimental and numerical studies;Chaos, Solitons & Fractals;2021-12

4. Bifurcation and chaotic behavior in the discrete BVP oscillator;International Journal of Non-Linear Mechanics;2021-05

5. Codimension two bifurcations of discrete Bonhoeffer–van der Pol oscillator model;Soft Computing;2021-01-08