Stochastic resonance and vibrational resonance in an excitable system: The golden mean barrier

Stan, Cristina; Cristescu, C.; Alexandroaei, D.; Agop, M.

doi:10.1016/j.chaos.2008.03.004

Cited by 24 publications

(10 citation statements)

References 24 publications

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“…An experimental demonstration of it in a bistable vertical-cavity surface-emitting laser [10][11][12], analog simulation of the overdamped Duffing oscillator [13], and the effect of an additive Gaussian white noise [13,14] were also reported. VR has also been found in excitable systems [15][16][17] and in small-world networks [18].…”

Section: Introductionmentioning

confidence: 93%

Theory and numerics of vibrational resonance in Duffing oscillators with time-delayed feedback

2011

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The influence of linear time-delayed feedback on vibrational resonance is investigated in underdamped and overdamped Duffing oscillators with double-well and single-well potentials driven by both low frequency and high frequency periodic forces. This task is performed through both theoretical approach and numerical simulation. Theoretically determined values of the amplitude of the high frequency force and the delay time at which resonance occurs are in very good agreement with the numerical simulation. A major consequence of time-delayed feedback is that it gives rise to a periodic or quasiperiodic pattern of vibrational resonance profile with respect to the time-delayed parameter. An appropriate time delay is shown to induce a resonance in an overdamped single-well system which is otherwise not possible. For a range of values of the time-delayed parameters, the response amplitude is found to be larger than in delay-time feedback-free systems.

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Section: Introductionmentioning

confidence: 93%

Theory and numerics of vibrational resonance in Duffing oscillators with time-delayed feedback

2011

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“…The response of the system to the input LF signal is evaluated by calculating the Fourier coefficient Q for the input frequency ω [15][16][17][18][19][20][21][22], defined as follows:…”

Section: Modeling and Simulationmentioning

confidence: 99%

“…VR has been theoretically demonstrated in a bistable system in the presence of additive white noise [16]. Experimentally, studies for VR have also been shown in an excitable electronic circuit [17], in analog simulations of the overdamped Duffing oscillator [18], and in a bistable optical cavity laser [19]. By use of experimental and numerical methods, Chizhevsky et al reported that VR was an effective method to improve the detection and recovery of weak subthreshold aperiodic binary signals in stochastic bistable systems [20].…”

Section: Introductionmentioning

confidence: 99%

Vibrational resonance induced by transition of phase-locking modes in excitable systems

Yang

Liu

et al. 2012

Phys. Rev. E

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We study the occurrence of vibrational resonance as well as the underlying mechanism in excitable systems. The single vibration resonance and vibration bi-resonance are observed when tuning the amplitude and frequency of high-frequency force simultaneously. Furthermore, by virtue of the phase diagram of low-frequency-signal-free FitzHugh-Nagumo model, it is found that each maxima of response measure is located exactly at the transition boundary of phase patterns. Therefore, it is the transition between different phase-locking modes that induces vibrational resonance in the excitable systems. Finally, this mechanism is verified in the Hodgkin-Huxley neural model. Our results provide insights into the transmission of weak signals in nonlinear systems, which are valuable in engineering for potential applications.

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“…In the dissipative approximation of the ESR the relation (15) becomes a Navier-Stokes type equation [41]:…”

Section: Satisfies the Relationmentioning

confidence: 99%

“…We remind that the Bohm formulation of quantum mechanism in terms of quantum potential [23][24][25][26][27][28] has been and still is, a continuous matter of dispute, often in rather philosophical terms above all concerning the fundamental meaning of quantum mechanics. Regarding concrete applications, such a theory has been used as a theoretical tool for understanding and interpreting several processes in different fields [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], from molecular physics to plasma physics, from scattering theory to simulation of quantum wires [44,45], to name a few.…”

Section: Introductionmentioning

confidence: 99%

System Dynamics Control through the Fractal Potential

et al. 2011

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Implications of the fractal potential in the system dynamics using an extended scale relativity model assuming the fractal character of the particle movements, are established. So, in the dissipative approximation of the model it is shown that the fractal potential comes from the non-differentiability of the space-time, i.e. by means of imaginary part of a complex speed field. In the dispersive approximation of the same model, the fractalization of the differential part of the complex speed field induces a normalized fractal potential which controls through coherence the system dynamics. In such context the type I superconductivity results: the temperature dependences of the superconducting parameter, the accumulator effect etc.

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Stochastic resonance and vibrational resonance in an excitable system: The golden mean barrier

Cited by 24 publications

References 24 publications

Theory and numerics of vibrational resonance in Duffing oscillators with time-delayed feedback

Theory and numerics of vibrational resonance in Duffing oscillators with time-delayed feedback

Vibrational resonance induced by transition of phase-locking modes in excitable systems

System Dynamics Control through the Fractal Potential

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