ON FRACTIONAL AND DISTRIBUTED ORDERS NONLINEAR CHAOTIC JERK MODELS AND THEIR CONTROL.

In this paper, we have introduced two versions of the jerk model. These versions are commensurate fractional and distributed orders. They appear in several applications of physics and engineering, e.g., laser physics, damped harmonic oscillators, and secure communications. The sufficient condition for the existence and uniqueness of the solution of commensurate fractional-order (CFO) jerk model is studied. We state and prove a theorem to test the dependence of the solutions of the CFO jerk model on initial conditions. The dynamics of the three versions of the jerk model are investigated. Using the largest Lyapunov exponent (LLE), we determine the values of the parameters at which these proposed versions have chaotic solutions. The linear feedback control is used to stabilize the chaotic solutions of these versions. Numerical simulations are used to show the chaotic solutions after control. [ABSTRACT FROM AUTHOR]