Analysis, Adaptive Control and Synchronization of a Seven-Term Novel 3-D Chaotic System with Three Quadratic Nonlinearities and its Digital Implementation in LabVIEW

Abstract

This research work proposes a seven-term novel 3-D chaotic system with three quadratic nonlinearities and analyses the fundamental properties of the system such as dissipativity, symmetry, equilibria, Lyapunov exponents and Kaplan-Yorke dimension. The phase portraits of the novel chaotic system simulated using MATLAB depict the strange chaotic attractor of the novel system. For the parameter values and initial conditions chosen in this work, the Lyapunov exponents of the novel chaotic system are obtained as �! = 2.71916, �! = 0 and �! = −13.72776. Also, the KaplanYorke dimension of the novel chaotic system is obtained as �!" = 2.19808. Next, an adaptive controller is designed to stabilize the novel chaotic system with unknown system parameters. Also, an adaptive controller is designed to achieve global chaos synchronization of two identical novel chaotic systems with unknown system parameters. Finally, an electronic circuit realization of the novel chaotic system is depicted using LabVIEW to confirm the feasibility of the theoretical chaotic model.

Keywords

• Chaos
• chaotic systems
• synchronization
• Lyapunov exponents
• Kaplan-Yorke dimension
• circuit simulation. ____________________________________________________________________________________