Analysis and Chaos Control and Synchronization of the Nonlinear Newton–Leipnik System Via Feedback Adaptive Control Techniques

Abstract

This paper presents the system analysis and chaos control synchronization of the Newton–Leipnik system. Uniqueness and existence solutions (equilibrium points or fixed points) of Newton–Leipnik system have been discussed and local analysis of the system at each equilibrium points is studied. Lyapunov exponents and Kaplan–Yorke dimensions, bifurcation diagrams and poincare sections are analyzed and plotted to establish the presence of chaos in the system. Control feedback techniques are simulated in the nonlinear Newton–Leipnik system. Controlling chaos of systems to find the desired result are established. Synchronization methodologies of two identical integer-order Newton–Leipnik systems are yielded applying adaptive control technologies which have been verified through plotting the graphs of tracking the trajectories of master to slave systems, parameter identification results and synchronization of error dynamics diagrams of Newton–Leipnik systems. These findings offer valuable insights and tools applicable to various scientific and technological domains. These results highlight the originality of our study and deepen our understanding of chaos in Newton–Leipnik systems, offering practical applications and enhanced insights for researchers and scientists in chaos analysis.