Experimental mastering of nonlinear dynamics in circuits by sporadic pulses

Ruiz, Pablo Jácome; Gutiérrez, José Manuel; Güémez, J.

doi:10.1016/j.chaos.2006.06.095

Cited by 6 publications

(3 citation statements)

References 22 publications

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“…For each set of parameters used in this work, the time step is always Δ = 0.005 and the simulations are done with variables and constant parameters in extended mode [16,17]. For each case, system (2) is integrated for a sufficiently long time and the transient is discarded with the time step being always Δ = 0.005.…”

Section: Dynamical Behavior Of the Mutuallymentioning

confidence: 99%

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Complex Dynamics and Synchronization in a System of Magnetically Coupled Colpitts Oscillators

Kana

Fomethe

Fotsin

et al. 2017

Journal of Nonlinear Dynamics

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We propose the use of a simple, cheap, and easy technique for the study of dynamic and synchronization of the coupled systems: effects of the magnetic coupling on the dynamics and of synchronization of two Colpitts oscillators (wireless interaction). We derive a smooth mathematical model to describe the dynamic system. The stability of the equilibrium states is investigated. The coupled system exhibits spectral characteristics such as chaos and hyperchaos in some parameter ranges of the coupling. The numerical exploration of the dynamics system reveals various bifurcations scenarios including period-doubling and interior crisis transitions to chaos. Moreover, various interesting dynamical phenomena such as transient chaos, coexistence of solution, and multistability (hysteresis) are observed when the magnetic coupling factor varies. Theoretical reasons for such phenomena are provided and experimentally confirmed with practical measurements in a wireless transfer.

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Section: Dynamical Behavior Of the Mutuallymentioning

confidence: 99%

“…Proposition 1. The synchronization problem for the magnetically coupled Colpitts system is to achieve the asymptote of the zero solution of the error system (17) in the sense that ‖ ( )‖ → 0, as → ∞ where ( = ; ; ; ).…”

Section: Synchronization Of Two Modified Colpitts Oscillatorsmentioning

confidence: 99%

Complex Dynamics and Synchronization in a System of Magnetically Coupled Colpitts Oscillators

Kana

Fomethe

Fotsin

et al. 2017

Journal of Nonlinear Dynamics

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“…To achieve two systems' synchronization, various synchronization control methods have been proposed since the pioneering work of Pecora and Carroll [5], which includes adaptive control [17], robust control [18], and others [19]. There are many practical synchronization experiments, including circuits [20,21] and laser systems [12,22]. Most of the existing synchronization control methods need to use the state information of the drive system at all times, except the impulse control [23].…”

Section: Introductionmentioning

confidence: 99%

Hyperchaos synchronization using univariate impulse control

et al. 2019

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Rössler and Chen systems with time delay are shown to be hyperchaotic, which exhibits a more complex dynamics, including multiple positive Lyapunov exponents and infinite dimension. The hyperchaos has better application potential where hyperchaos synchronization is concerned. Univariate impulse control requires smaller perturbation to the response system, thus promising better performance. However, synchronization of two hyperchaotic systems using this control method is a challenging task due to the difficulty to guarantee synchronization stability using a minimum number of manipulated variables. In this paper, a univariate impulse control method is proposed for the synchronization of two hyperchaotic dynamics generated by time delay. A theorem is developed and proved to provide the sufficient conditions for the synchronization of time delay systems using the univariate impulse control. The upper bound of the impulse interval is proved to guarantee the asymptotic synchronization. Simulation and circuit experiment show the correctness of the analysis and the feasibility of the proposed method.

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