Dynamics of a Hybrid Circuit System With Lossless Transmission Line

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.