A Modified Lorenz Chaotic System And Its Circuit Simulation

Over the last four decades, chaos as a very interesting phenomenon has been intensively investigated. The phenomenon is common; it has been detected in a large number of dynamic systems of various physical natures and includes extremely abundant contents. In 1963, Lorenz found the first canonical chaotic attractor in three-dimensional autonomous system. Recently some new chaotic system has been introduced, which are all particular case of the so-called generalized Lorenz canonical form (GLCF).In the thesis, a new chaotic system which we have called a modified Lorenz system is proposed. Some basic dynamical properties, Continuous spectrum, Lyapunov exponents, fractal dimension and strange attractor of this new chaotic system are studied; the chaotic attractor obtained from this new system according to the detailed numerical as well as theoretical analysis is also the butterfly-shaped attractor which is similar to Lorenz attractor, but not equivalent chaotic attractor. And then, an electronic circuit is designed use Electronics Workbench (EWB) in order to confirm the every state and it accordance with the results of simulations.Research efforts have investigated chaos control and chaos synchronization problems in many physical chaotic systems. Nowadays, different techniques and methods have been proposed to achieve chaos control and chaos synchronization such as linear and non-linear feedback control. Based on the Lyapunov stability theory, a novel adaptive control law is derived for the synchronization of this modified Lorenz system with known and unknown system parameters. In Chapter 4, the method of chaos control which I adopt to control this new chaotic system to the equilibrium point and period is linear feedback control. In Chapter 5, chaos self-synchronization control and isomer synchronization are investigated. The two modified system which is confirmed not only by simulating but also by experimenting, similarly, two different chaotic systems which is also confirmed not only by simulating but also by experimenting.