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 pro...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi-Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/2178031 |
| Summary: | 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. |
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| ISSN: | 1076-2787 1099-0526 |