J.L. Hindmarsh, R.M. Rose introduced the concept of neuronal burst. In this paper, synchronization is investigated for the construction of a model of neuronal burst using backstepping control with recursive feedback. Synchronization for a model of neuronal bursting system is established using Lyapunov stability theory. The backstepping scheme is a recursive procedure that links the choice of a Lyapunov function with the design of a controller. The backstepping control method is effective and convenient to synchronize identical systems. Numerical simulations are furnished to illustrate and validate the synchronization result derived in this paper.
This paper investigates the backstepping control design with novel feedback input ap-proach for controlling chaotic systems to guarantee the complete synchronization as well asthe anti-synchronization of chaotic systems, viz. n–scroll Chua (K. Wallace et.al. 2001) andLur’e chaotic systems. Our theorems on hybrid synchronization for n–scroll Chua and Lur’e(J.Suyken et.al. 1997) chaotic systems is established using Lyapunov stability theory. Based onthe Lyapunov function, the backstepping control is determined to tune the controller gain basedon the precalculated feedback control inputs. The backstepping scheme is recursive procedurethat links the choice of a Lyapunov function with the design of a controller and guaranteesglobal stability performance of strict-feedback chaotic systems. Since the Lyapunov exponentsare not required for these calculations, the backstepping control method is effective and conve-nient to synchronize the chaotic systems. Mainly this technique gives the flexibility to constructa control law. Numerical simulations are also given to illustrate and validate the hybrid synchro-nization results derived in this paper.