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Dynamical analysis, stabilization and discretization of a chaotic fractional-order GLV model

机译：混沌分数阶GLV模型的动力学分析，稳定和离散化

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摘要

In this paper, the fractional-order generalized Lotka-Volterra (GLV) model and its discretization are investigated qualitatively. A sufficient condition for existence and uniqueness of the solution of the proposed system is shown. Analytical conditions of the stability of the system's three non-negative steady states are proved. The conditions of the existence of Hopf bifurcation in the fractional-order GLV system are discussed. The necessary conditions for this system to remain chaotic are obtained. Based on the stability theory of fractional-order differential systems, a new control scheme is introduced to stabilize the fractional-order GLV system to its steady states. Furthermore, the analytical conditions of stability of the discretized system are also studied. It is shown that the system's fractional parameter has effect on the stability of the discretized system which shows rich variety of dynamical analysis such as bifurcations, an attractor crisis and chaotic attractors. Numerical simulations are used to support the analytical results.
机译：本文定性研究了分数阶广义Lotka-Volterra（GLV）模型及其离散化。给出了所提出系统的解的存在性和唯一性的充分条件。证明了系统三个非负稳态的稳定性的分析条件。讨论了分数阶GLV系统中Hopf分支的存在条件。获得该系统保持混沌的必要条件。基于分数阶微分系统的稳定性理论，提出了一种新的控制方案，将分数阶GLV系统稳定在稳态。此外，还研究了离散系统稳定性的分析条件。结果表明，系统的分数参数对离散化系统的稳定性有影响，离散化系统表现出丰富的动力学分析，如分叉，吸引子危机和混沌吸引子。数值模拟用于支持分析结果。

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