Filtering by nonlinear systems

Abstract

Synchronization of nonlinear systems forced by external signals is formalized as the response of a nonlinear filter. Sufficient conditions for a nonlinear system to behave as a filter are given. Some examples of generalized chaos synchronization are shown to actually be special cases of nonlinear filtering.

A simple filter Lorenz electronic circuit

“…Electronic circuits used for synchronization include Lorenz, Chua, Chen, and so on [12][13][14]. These circuits in communication systems are used as master and slave systems, where the slave system can be regarded as a filter [15]. Over the past decade, fractional order filters have been implemented.…”

“…The work presented in Ref. [15] deals with synchronization phenomena and shows that the slave system behaves like a filter. In this work, the Lorenz system is presented as a filter.…”

“…A demonstration of this is given in Ref. [15]. Other research on Lorenz systems have been conducted: [19] uses Presnov decomposition to address the synchronization problem of fractional order Lorenz families, [20] uses CMOS technology to synthesize a mathematical Lorenz model, and [21] analyzes the system through rotation.…”

“…Other research on Lorenz systems have been conducted: [19] uses Presnov decomposition to address the synchronization problem of fractional order Lorenz families, [20] uses CMOS technology to synthesize a mathematical Lorenz model, and [21] analyzes the system through rotation. In this investigation, we use the work [15] to replace the Lorenz electronic circuit according to the equation of x state. In Ref.…”

“…To achieve this, we use a Lorenz system in the filtering approach proposed in Ref. [15] and decompose it into two cascaded subsystems. The first subsystem corresponds to the equation of state x, and the second subsystem corresponds to the remaining equations y and z.…”