Analysis, Control, and Synchronization of a 3-D Novel Jerk Chaotic System with Two Quadratic Nonlinearities

Abstract

Abstract. In this research work, a seven-term 3-D novel jerk chaotic system with two quadratic nonlinearities has been proposed. The basic qualitative properties of the novel jerk chaotic system have been described in detail. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel jerk chaotic systems with two unknown parameters. MATLAB simulations have been shown in detail to illustrate all the main results developed for the 3-D novel jerk chaotic system.

A New Hamiltonian Chaotic System with Coexisting Chaotic Orbits and its Dynamical Analysis

“…Chaotic systems have applications in several areas of science and engineering ([1]- [2]). Some common applications of chaos theory can be mentioned such as finance systems ( [3]- [6]), weather models ([7]- [9]), biological models ([10]- [13]), neural networks ( [14]- [16]), chemical reactions ( [17]- [20]), ecological models ( [21]- [23]), oscillations ( [24]- [30]), jerk systems ( [31]- [34]), encryption ( [35]- [38]), robotics ([39]- [40]), circuits ( [41]- [52]), etc.…”

A new three-dimensional chaotic system with a hidden attractor, circuit design and application in wireless mobile robot

“…Some well-known examples of self-excited chaotic attractors are Chen system [15], Lorenz system [16], Sundarapandian systems [17,18], Pehlivan system [19], Akgul system [20], etc.…”

A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control

“…Many new chaotic systems have been also discovered like Li system [15], Sundarapandian systems [16,17], Vaidyanathan systems [18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33], Pehlivan system [34], Tacha system [35], Jafari system [36], Sampath system [37], Pham systems [38,39,40,41,42,43,44], Volos system [45], Akif system [46], etc.…”