n : m Synchronization of Periodic Oscillations

Balanov, A. G.; Janson, Natalia B.; Postnov, Dmitry E.; Sosnovtseva, Olga

doi:10.1007/978-3-540-72128-4_6

Cited by 14 publications

(28 citation statements)

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“…Phase transitions for gradient system with local interactions were studied in [21,22]. Synchronization has been extensively discussed in the scientific literature, see [17,[23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Response theory and phase transitions for the thermodynamic limit of interacting identical systems

2020

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We study the response to perturbations in the thermodynamic limit of a network of coupled identical agents undergoing a stochastic evolution which, in general, describes non-equilibrium conditions. All systems are nudged towards the common centre of mass. We derive Kramers–Kronig relations and sum rules for the linear susceptibilities obtained through mean field Fokker–Planck equations and then propose corrections relevant for the macroscopic case, which incorporates in a self-consistent way the effect of the mutual interaction between the systems. Such an interaction creates a memory effect. We are able to derive conditions determining the occurrence of phase transitions specifically due to system-to-system interactions. Such phase transitions exist in the thermodynamic limit and are associated with the divergence of the linear response but are not accompanied by the divergence in the integrated autocorrelation time for a suitably defined observable. We clarify that such endogenous phase transitions are fundamentally different from other pathologies in the linear response that can be framed in the context of critical transitions. Finally, we show how our results can elucidate the properties of the Desai–Zwanzig model and of the Bonilla–Casado–Morillo model, which feature paradigmatic equilibrium and non-equilibrium phase transitions, respectively.

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Section: Introductionmentioning

confidence: 99%

Response theory and phase transitions for the thermodynamic limit of interacting identical systems

2020

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“…1(a), the graph of the transverse Lyapunov exponent exponent vs. coupling parameter has not been extended beyond ε c2 . In passing, it may be mentioned that the above discussion has nothing to do with the noninvertibility of transformation (12). Even a linear (hence invertible) transformation would not have necessarily resulted in generalized synchronization because mere equivalence between the drive and the driven does not guarantee it.…”

Section: A the Rössler And Transformed Rössler Systemmentioning

confidence: 98%

“…10 In the last two decades, the theories on synchronization in chaotic systems has attracted a lot of attention. 11,12 The phenomenon of synchronization has been systematically classified into many types, viz., complete or identical synchronization, 13,14 phase synchronization, 15,16 imperfect phase synchronization, burst synchronization, 17,18 lag synchronization, 19 intermittent lag synchronization, 19,20 generalized synchronization (either weak or strong) [21][22][23][24] and so on. Researchers have tried to invent a unified definition to encompass these different types, and also have contemplated extending the definition to infinite dimensional systems described by partial differential equations and/or systems where noise is present.…”

Section: Introductionmentioning

confidence: 99%

Synchronizing noisy nonidentical oscillators by transient uncoupling

Tandon

Schröder

Mannattil

et al. 2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional relationship between them-a phenomenon termed "generalized synchronization." Here, we show that the concept of transient uncoupling, recently introduced for synchronizing identical units, also supports generalized synchronization among nonidentical chaotic units. Generalized synchronization can be achieved by transient uncoupling even when it is impossible by regular coupling. We furthermore demonstrate that transient uncoupling stabilizes synchronization in the presence of common noise. Transient uncoupling works best if the units stay uncoupled whenever the driven orbit visits regions that are locally diverging in its phase space. Thus, to select a favorable uncoupling region, we propose an intuitive method that measures the local divergence at the phase points of the driven unit's trajectory by linearizing the flow and subsequently suppresses the divergence by uncoupling.

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“…The solution of (1) for transient and steady-state conditions was considered in [4,5] as well, and it is known that for steady state the solution is x = A sin oJol (2) where A = 2�00 / O 2 . Van der Pol oscillator is used very frequently as an approximation for oscillating systems (there is an opinion [5], shared by these authors, that it is sufficient for all electronic applications). The linear damping term -21 00 1 is usually well defmed, but the nonlinear positive term 2 0 2 is better to obtain from experimental or simulated data [6] to avoid the discrepancy between calculated and simulated or experimental results.…”

Section: Theory Of Regenerative Amplifiermentioning

confidence: 99%

Regenerative current amplifier using van der Pol approximation

Filanovsky

Oliveira

2011

2011 IEEE 54th International Midwest Symposium on Circuits and Systems (MWSCAS)

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When van der Pol oscillator linear damping parameter is positive then this oscillator becomes a nonlinear resonant amplifier of high sensitivity for small ac signals with the frequencies located in the vicinity of the oscillator natural frequency. The gain characteristic of this amplifier is similar to the gain characteristic of logarithmic amplifier; the sensitivity is high for small signals and, due to the nonlinear damping parameter, is reduced for the signals of higher amplitudes. Application of this amplifier in regenerative receiver requires a precise control of the linear term, i.e. the Q-factor of linear low level signal operation. The proposed amplifier is realized using a modified active inductor circuit with compensation of resistive component in input admittance; this approach provides the required high value and good control of Q-factor. The simulations of amplifier selectivity characteristics are given for the design example using 130 nm CMOS technology.

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n : m Synchronization of Periodic Oscillations

Cited by 14 publications

References 0 publications

Response theory and phase transitions for the thermodynamic limit of interacting identical systems

Response theory and phase transitions for the thermodynamic limit of interacting identical systems

Synchronizing noisy nonidentical oscillators by transient uncoupling

Regenerative current amplifier using van der Pol approximation

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