Automatic Chaos Control of the Two-Dimensional Burger Map Through Genetic Algorithms

Chaotic systems are highly sensitive to initial conditions, where even infinitesimal differences in starting points can lead to drastically different long-term behaviors. Since the 1990s, researchers have discovered that chaos can be regulated, a concept known as chaos control. In this paper, we describe a method for automatic chaos control of chaotic maps, aiming to stabilize chaotic dynamics into a periodic orbit with a predefined period. Our approach builds upon an existing technique that applies control pulses of constant pulse intensity and frequency, both being adjustable parameters of the method. We formulate this as a complex optimization problem involving multiple variables, nonlinearity, and a multimodal landscape, solved through a genetic algorithm approach. To validate our method, we conduct computational experiments using the 2D Burger map under different parameter configurations. The results confirm that our approach stabilizes chaotic behavior, showing a promising potential for automating chaos control in dynamical systems.