Oscillations in First‐Order, Continuous‐Time Systems via Time‐Delay Feedback

A technique to generate (periodic or nonperiodic) oscillations systematically in first‐order, continuous‐time systems via a nonlinear function of the state, delayed by a certain time d, is proposed. This technique consists in choosing a nonlinear function of the delayed state with some passivity properties, tuning a gain to ensure that all the equilibrium points of the closed‐loop system be unstable, and then imposing conditions on the closed‐loop system to be semipassive. We include several typical examples to illustrate the effectiveness of the proposed technique, with which we can generate a great variety of chaotic attractors. We also include a physical example built with a simple electronic circuit that, after applying the proposed technique, displays a similar behavior to the logistic map.