Dynamical study of a novel three-dimensional and generalized chaotic system. (1st July 2022) - Saifullah, Sayed; Doungmo Goufo, Emile Franc; Ali, Amir
Abstract: In this manuscript, a new three-dimensional continuous chaotic model is presented based on the modification in the Lorenz system. The dynamical aspects of the complex system are investigated, covering equilibrium points and linear stability, dissipation, phase portraits, Poincaré mapping, Lyapunov exponent, attractor projection, bifurcations, time series analysis, and sensitivity. The model is also studied numerically using the Haar wavelet scheme with Caputo fractional derivative. The positive exponent reveals that the system is chaotic. The symmetric limit cycle and butterfly type attractors are observed because the trajectories of the model ultimately progress to a bounded region. The existence of the chaotic attractor is shown by Poincaré section. In the Poincaré section, the kindling is integrated and connected as a single attractor. From the sensitivity analysis of the system, it is noted the system is dependent on the initial conditions that show chaos in the system. The evolution of the attractor is depicted by fixing the first two parameters and varying the third. The theoretical and numerical studies exhibit that the model has complex dynamics with certain stimulating physical characteristics.