Combination anti-synchronization for chaos generated by generalized Lotka-Volterra biological systems using parameter identification method

Abstract

In this research article, we systematically describe a methodology to investigate combination anti-synchronization (CAS) among chaotic generalized three species Lotka-Volterra (GLV) biological system. The well-known biological model of two species, predator and prey, was firstly outlined by Lotka and Volterra in the 1920s. This model represents the interaction among two species predator-prey which contains a system of nonlinear ordinary differential equations (ODEs). We here consider two predators and one prey population existing in the considered GLV model. Initially, a parameter identification method, also known as adaptive control method (ACM), has been proposed which is based on Lyapunov stability theory (LST). The biological adaptive control law (ACL) for achieving global and asymptotic stability of the state variables of the considered biological system with unknown parameters has been derived. Furthermore, numerical simulations (NM) are performed for demonstrating the effectiveness and feasibility of the considered scheme utilizing MATLAB software. In addition, a comparison analysis has been done. Exceptionally, the obtained theoretical results are in complete agreement with computational results. The considered technique has numerous applications in the area of secure communications and image encryption.