Periodicity windows in a dynamical system with a delayed feedback

Vallée, Réal; Delisle, Claude

doi:10.1103/physreva.34.309

Cited by 39 publications

(14 citation statements)

References 11 publications

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“…Although bistability has been previously noted in such systems, 9,20,25,22,21 we report here on the sensitivity of the solution behavior on perturbations of the initial function. For the logistic DDE (Sec.…”

Section: Discussionmentioning

confidence: 83%

Solution multistability in first-order nonlinear differential delay equations

Losson

Mackey

Longtin

1993

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The dependence of solution behavior to perturbations of the initial function (IF) in a class of nonlinear differential delay equations (DDEs) is investigated. The structure of basins of attraction of multistable limit cycles is investigated. These basins can possess complex structure at all scales measurable numerically although this is not necessarily the case. Sensitive dependence of the asymptotic solution to perturbations in the initial function is also observed experimentally using a task specific electronic analog computer designed to investigate the dynamics of an integrable first-order DDE.

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Section: Discussionmentioning

confidence: 83%

Solution multistability in first-order nonlinear differential delay equations

Losson

Mackey

Longtin

1993

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…] for the Vallee model [28], f (x) = μ sin x for Ikeda model [26], etc. We take another system with parameter mismatch from (1),…”

Section: Nonlinear Observer-based Projective-dual Synchronization Schemementioning

confidence: 99%

Projective-dual synchronization in delay dynamical systems with time-varying coupling delay

Ghosh¹

2011

Nonlinear Dyn

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The existence of projective-dual-anticipating, projective-dual, and projective-dual-lag synchronization in a coupled time-delayed systems with modulated delay time is investigated via nonlinear observer design approach. Transition from projectivedual-anticipating to projective-dual synchronization and from projective-dual to projective-dual-lag synchronization as a function of variable coupling delay τ p (t) is discussed. Using Krasovskii-Lyapunov stability theory, a general condition for projective-dual synchronization is derived. Numerical simulations on the chaotic Ikeda and Mackey-Glass systems are given to demonstrate the effectiveness of the theoretical results.

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“…In the past, fair agreement between experimental results and numerical simulations has been obtained, allowing the checking of a good many theoretical predictions [6][7][8][9][10][11][12][17][18][19][20]. However, a fundamental knowledge of the mechanisms ruling stability is lacking.…”

Section: Introductionmentioning

confidence: 95%

“…where a dot means differentiation with respect to time t, r is the delay, x represents the output signal, and the function f accounts for the nonlinear response of the device and may depend on a number of controllable parameters [13][14][15]20]. Similar equations (or systems thereof) also arise as models for electronic circuits [21] or neuron systems [3,4].…”

Section: Introductionmentioning

confidence: 99%