Controlling Chaos in the Lozi Map Using Hidden Variables: A Novel Approach for Stability Enhancement

Abstract

In this paper, we provide a novel 3D system that demonstrates the existence of a hidden attractor. Although equilibrium points are present in the system, this hidden attractor cannot be found by examining equilibrium points or their surroundings, in contrast to self-excited attractors. Differential equation theory explains this behavior  by showing that the system has intricate dynamics that are not directly dependent on equilibrium points. We added a hidden variable to the system to make it more complex and improve its stability by adding the following equation to the original system: zn+1=wzn+r3xn, where the hidden variable interacts with the original system through control parameters r1, r2, and r3, increasing chaos or improving the system stability. where it appeared us more complex dynamic behaviors