**Pattrawut Chansangiam**

Department of Mathematics, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Bangkok 10520, Thailand; pattrawut.ch@kmitl.ac.th; Tel.: +66-9352-666-00

Received: 25 September 2020; Accepted: 28 October 2020; Published: 30 October 2020

**Abstract:** This paper investigates the chaotic behavior of a modified jerk circuit with Chua's diode. The Chua's diode considered here is a nonlinear resistor having a symmetric piecewise linear voltage-current characteristic. To describe the system, we apply fundamental laws in electrical circuit theory to formulate a mathematical model in terms of a third-order (jerk) nonlinear differential equation, or equivalently, a system of three first-order differential equations. The analysis shows that this system has three collinear equilibrium points. The time waveform and the trajectories about each equilibrium point depend on its associated eigenvalues. We prove that all three equilibrium points are of type saddle focus, meaning that the trajectory of (*x*(*t*), *y*(*t*)) diverges in a spiral form but *z*(*t*) converges to the equilibrium point for any initial point (*x*(0), *y*(0), *z*(0)). Numerical simulation illustrates that the oscillations are dense, have no period, are highly sensitive to initial conditions, and have a chaotic hidden attractor.

**Keywords:** chaos theory, electrical circuit analysis, jerk circuit, Chua's diode, system of differential equations, hidden attractor.

**PACS:** 02.10.Ud; 02.30.Hq; 05.45.Pq; 84.32.-y
