SYNCHRONIZATION OF MODIFIED CHAOTIC COLPITTS OSCILLATOR USING NON-LINEAR FEEDBACK METHOD

Abstract

A modified 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 work has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. Moreover, chaos control, stability and synchronization of such a system have been dealt with.

Specification

INTRODUCTION
A chaotic system with chaotic attractor is posing several challenges thereby making the study quite interesting. A non-linear dynamical system exhibiting complex and unpredictable behavior is called chaotic system. The parameter values are varying with range and the sensitivity depends on initial conditions. These are the remarkable properties of chaotic systems. Sometimes, the chaotic systems are deterministic and they have long-term unpredictable behavior. While chaotic systems are highly sensitive, their sensitivity depends on their initial conditions. The chaotic nature is one of the qualitative properties of a dynamical system. The controlling of the chaotic systems may be accomplished in three ways such as stabilization of unstable periodic motion "contained" in the chaotic set, suppression of chaotic behavior by external forcing like periodic noise, periodic parametric perturbation and algorithm of various automatic control like feedback etc. There exist two ways for the application of controls in a chaotic system. The first one is the change of attractor of the system. The second one is the change in the point position of the phase space for the system which is a constant value in its parameter. A continuous, repeated and alternating wave production without any input is an oscillator. Converting power supply to an alternating current signal is one of the primary properties of oscillators. The signal of feedback containing a pair of coils and an inductive divider in the server is called Colpitts oscillator. Due to some parametric change and the variation of input, the chaotic nature may occur in Colpitts oscillators. In this paper, a modified chaotic Colpitts oscillator is proposed.
BACK GROUND
The application part is in secure communication systems. It acts as protection wall to avoid hacking information in communication.
METHODS
The non-linear feedback method control technique is used to control the system. Synchronization, the non-linear control is utilized. Numerical simulations support the results. MATLAB is used for numerical simulation.
The synchronization of modified Colpitts oscillator is now taken up. The drive-response formalism is utilized. The identical synchronization is elaborated between the modified Colpitts oscillators.
The chaos synchronization basically requires the global asymptotic stability of the error dynamics.
CONCLUSION
The Colpitts oscillator with logarithmic non-linearity in analyzed. The qualitative properties of the modified Colpitts oscillator is analyzed in this study. It exhibits the hyperchaotic nature for some specified initial condition of the parameter. By Wolf method, the Lyapunov exponent's is calculated. For some initial conditions, it exhibits the dissipative nature. The non-linear feedback method control technique is used to control the system. Synchronization, the non-linear control is utilized. Numerical simulations support the results. MATLAB is used for numerical simulation. The application part is secure communication.





We Claim:
1. The non-linear feedback method is used to control the system. For synchronization, the nonlinear control is utilized. Numerical simulations are done by using matlab.
2. We claim that through this report the analysis of the proper data guidance the academics and industry wise segments can be improved gradually.

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