SONGKLANAKARIN JOURNAL OF SCIENCE & TECHNOLOGY

Volume 42, No. 03, Month MAY, Year 2020, Pages 678 - 687

Mathematical analysis for classical chua s circuit with two nonlinear resistors

Natchaphon Limphodaen and Pattrawut Chansangiam

Abstract Download PDF

We formulate a mathematical model for the classical Chua’s circuit with two nonlinear resistors in terms of a system of nonlinear ordinary differential equations. The existence of two nonlinear resistors implies that the system has three equilibrium points. The behaviour of the trajectory in a neighbourhood of each equilibrium point depends on the eigenvalues of the system. The eigenvalues can be obtained from a cubic polynomial equation. It turns out that all possible solutions of the cubic equation lead to six types of equilibrium points, namely, stable node, unstable node, saddle node, stable focus node, unstable focus node, saddle focus node. The chaotic behaviour of the circuit occurs when the equilibrium point is a stable focus node or a saddle focus node. The hidden attractor of our Chua’s system is localized through a suitable initial point.

Keywords

chaos theory, circuit analysis, Chua’s circuit, nonlinear resistors, hidden attractor

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