数学
相图
分叉
混乱的
应用数学
离散化
控制理论(社会学)
中央歧管
数学分析
霍普夫分叉
非线性系统
计算机科学
物理
控制(管理)
量子力学
人工智能
作者
Md. Jasim Uddin,Chandra Nath Podder
标识
DOI:10.1142/s1793524523500511
摘要
In this paper, the Caputo fractional derivative is assumed to be the prey–predator model. In order to create Caputo fractional differential equations for the prey–predator model, a discretization process is first used. The fixed points of the model are categorized topologically. We identify requirements for the fixed points of the suggested prey–predator model’s local asymptotic stability. We demonstrate analytically that, under specific parametric conditions, a fractional order prey–predator model supports both a Neimark–Sacker (NS) bifurcation and a Flip bifurcation. We present evidence for NS and Flip bifurcations using central manifold and bifurcation theory. The parameter values and the initial conditions have been found to have a profound impact on the dynamical behavior of the fractional order prey–predator model. As the bifurcation parameter is increased, the system displays chaotic behavior. Numerical simulations are shown to demonstrate chaotic behaviors like bifurcations, phase portraits, invariant closed cycles, and attractive chaotic sets in addition to validating analytical conclusions. The suggested prey–predator dynamical system’s chaotic behavior will be controlled by the OGY and hybrid control methodology, which will also visualize the chaotic state for various biological parameters.
科研通智能强力驱动
Strongly Powered by AbleSci AI