In this paper the fractional version of the proposed integer order chaotic ecological system is studied. Here chaos has been observed in the competitive ecological model due to linear and nonlinear interactions among various species considering shortage of food resources. The system being important constituent of the food supply chain is analyzed using tools of dynamics viz. Lyapunov dynamics, bifurcation diagrams, existence and uniqueness of solution, the fixed point analysis and effect of fractional order on the dynamics of the system. In the presence of uncertainties and disturbances the chaos in the F.O. ecological model is controlled using adaptive SMC theory about its two fixed points. Numerical illustrations have been provided using MATLAB.

本文研究了提出的整数阶混沌生态系统的分数形式。考虑到粮食资源的短缺，由于各种物种之间的线性和非线性相互作用，在竞争性生态模型中已观察到混乱。该系统是食品供应链的重要组成部分，使用动力学工具进行了分析。Lyapunov动力学，分岔图，解的存在性和唯一性，不动点分析以及分数阶对系统动力学的影响。在存在不确定性和干扰的情况下，使用自适应SMC理论控制FO生态模型的两个固定点，从而控制混沌。使用MATLAB提供了数字插图。