On Chaotic Behavior of a Class of Linear Systems with Memristive Feedback Control

The contribution is concerned on structural properties and general features of the new ideal circuit element, a memristor. By definition, a memristor relates the charge q and the magnetic flux φ in a circuit, and complements a resistor R, a capacitor C, and an inductor L as an ingredient of ideal electrical circuits. The definition of the memristor is based solely on fundamental circuit variables, similar to the resistor, capacitor, and inductor. Unlike conventional electrical circuit elements, memristors do not belong to the class of linear time-invariant systems, because a linear time-invariant memristor is simply a conventional resistor. In the paper a special class of nonlinear feedback systems consisting of finite dimensional linear dynamical subsystems controlled by a memristance-based feedback controller with static nonlinearity is investigated. Key-Words: Memristance, feedback, nonlinearity, state space energy, chaotic behavior, dissipation structure.