Evolving new chaotic system with no equilibrium point by evolutionary algorithm

Abstract

Recently, it is found that some systems without real equilibrium point can also generate chaos (known as Chaos with hidden attractor). In this project, it is to design an evolutionary algorithm using C++ to obtain this special kind of chaotic systems. Assuming a 3rd dimensional continuous-time system and limiting some particular forms of the state equations, chaotic systems can be found by evolving the coefficients. The system performance is governed by a fitness value, which is determined by the Lyapunov Exponents of the obtained system. Based on designed genetic operators, a population of new chaotic systems with hidden attractors can be obtained through the optimization process. In addition, a graphical user interface (GUI) is developed to provide user friendly environment to view the chaotic systems obtained using MATLAB GUI development environment. By fetching data from log file outputted by the C++ program, the obtained chaotic systems can be viewed graphically with different axis including coordinate x, y, z and time. Options such as starting time, ending time and starting point can also be set to view different state of the system.