Open AccessA New Chaotic Jerk System with Three Nonlinearities and Synchronization via Adaptive Backstepping Control
Author(s) -
Sundarapandian Vaidyanathan,
Sifeu Takougang Kingni,
Aceng Sambas,
Mohamad Afendee Mohamed,
Mustafa Mamat
Publication year - 2018
Publication title -
international journal of engineering and technology
Language(s) - English
Resource type - Journals
ISSN - 2227-524X
DOI - 10.14419/ijet.v7i3.15378
Subject(s) - jerk , control theory (sociology) , chaotic , synchronization of chaos , backstepping , attractor , phase portrait , lyapunov exponent , saddle , nonlinear system , synchronization (alternating current) , computer science , mathematics , physics , topology (electrical circuits) , adaptive control , bifurcation , mathematical analysis , control (management) , artificial intelligence , classical mechanics , mathematical optimization , acceleration , quantum mechanics , combinatorics
Jerk systems are popular in mechanical engineering and chaotic jerk systems are used in many applications as they have simple structure and complex dynamic properties. In this work, we report a new chaotic jerk system with three nonlinear terms. Dynamical properties of the chaotic jerk system are analyzed through equilibrium analysis, dissipativity, phase portraits and Lyapunov chaos exponents. We show that the new chaotic jerk system has a unique saddle-focus equilibrium at the origin. Thus, the new chaotic jerk system has a self-excited strange attractor. Next, global chaos synchronization of a pair of new chaotic jerk systems is successfully achieved via adaptive backstepping control.