Analysis and Control of Chaos in Simple 3D Autonomous System with Exponential Nonlinearity

A new three-dimensional autonomous chaotic system is introduced in this paper. Our considered system is algebraically simple such that it possesses six terms with only one exponential nonlinear term. From numerical investigations, it is observed that our considered system is capable to show Rössler-like dynamical features. Stability of equilibrium solutions is discussed with linear stability analysis, and conditions for the Hopf bifurcation is determined. On the other hand, non-local characteristics of the system also identified with the use of nonlinear analysis tools such as phase portraits, Lyapunov exponents and bifurcation diagrams. Finally, an adaptive feedback control method is applied to our considered system, and it is shown that for suitable feedback gains the chaotic behaviour is stabilized.