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Abstract

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.

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Authors and Affiliations

Suresh Rasappan
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Abstract

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.
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Authors and Affiliations

Suresh Rasappan
Sundarapandian Vaidyanathan
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Abstract

The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.
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Bibliography

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Authors and Affiliations

Suresh Rasappan
1
K.A. Niranjan Kumar
1

  1. Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, Avadi, Chennai-62, India

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