Abstract
In this paper, a hybrid circuit system composed of a Chua's circuit with lossless transmission line and a RC oscillating circuit is considered. First, the equations describing the hybrid circuit system are reduced to a set of hybrid equations made up of a delayed neutral-type differential equation and a differential equation. By constructing the appropriate Lyapunov function, a novel condition of global stability is derived, which depends on the lower bound of fi(x)/x. Using the length of transmission line as the bifurcation parameter, the conditions of local stability and Hopf bifurcation are obtained. Finally, the realization of our proposed circuit is given and two examples are given to verify the obtained theoretical analysis by using Matlab and Multisim14.0.
Highlights
Chua’s circuit is one of the significant nonlinear circuit systems, which was proposed by Leon O
Recently, with the progress of electronic technology, nonlinear electronic devices are widely used in the hybrid circuit system, which leads to a large number of nonlinear phenomena in hybrid circuit system such as oscillation, quasioscillation, chaos and so on
It is found that these dynamic behaviors generated by hybrid circuit system have many applications such as image encryption [1]–[3], secure communication [4]–[6], wave filter [7] and so on
Summary
Chua’s circuit is one of the significant nonlinear circuit systems, which was proposed by Leon O. It is well known that Chua’s circuit has rich dynamic behaviors such as multi-stability, periodic solution, quasi periodic solution, chaos and so on. It is of great practical significance to study this kind of coupled circuit composed of TDCC and RC oscillating circuit. Few works study the dynamics of hybrid circuit system composed of TDCC and RC oscillating circuit. The main contribution of this paper is as follows: 1) A hybrid circuit system composed of a Chua’s circuit with lossless transmission line and a RC oscillating circuit is proposed.
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