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

• Main Authors: Abimael Salcedo, Joaquin Alvarez
• Format: Article
• Language: English
• Published: Hindawi-Wiley 2018-01-01
• Series: Complexity
• Online Access: http://dx.doi.org/10.1155/2018/2178031

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.