A new two-scroll chaotic attractor with three quadratic nonlinearities, its adaptive control and circuit design

A New Four-Scroll Chaotic System with a Self-Excited Attractor and Circuit Implementation

“…Some classical examples of two-scroll chaotic attractors can be cited as Lorenz system [43], Lü system [44] and Tigan system [45]. Some recent examples of two-scroll chaotic attractors can be mentioned as Lien system [46] [59]. In this paper, we report the finding of a new four-scroll chaotic system with four nonlinear terms.…”

Analysis, dynamics and adaptive control synchronization of a novel chaotic 3-D system

“…Substituting (27) into (26), we get which is a negative definite function on R 3 . Hence, by the Lyapunov stability theory [34], it follows that e i (t) ⟶ 0 as t ⟶ ∞ for i = 1, 2, 3.…”

“…Hence, we have proved the following theorem. (15) and (16) with unknown parameters are globally and exponentially synchronized for all initial conditions by the adaptive feedback control law (20) and the parameter update law (27), were k 1 , k 2 , k 3 are positive constants.…”

“…In Figs. 20, 21 and 22, the synchronization of the states of the master system (15) and slave system (16) is depicted, when the adaptive control law (20) and parameter update law (27) are implemented. In Fig.…”

“…This control method differs from other control methods because it does not require advance information about the limits on these uncertain or time-varying parameters because it relates to a control law that changes itself. Recently, many papers are available on synchronization of chaotic systems using this method of control [20][21][22][23][24][25][26][27][28][29][30][31]. This paper is organized as follows: The second section deal with the description and some properties of the novel chaotic system.…”