Stable Limit Cycle

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Alessandro Costalunga - One of the best experts on this subject based on the ideXlab platform.

Luca Consolini - One of the best experts on this subject based on the ideXlab platform.

Juergen Jost - One of the best experts on this subject based on the ideXlab platform.

  • the stochastic fitzhugh nagumo neuron model in the excitable regime embeds a leaky integrate and fire model
    Journal of Mathematical Biology, 2019
    Co-Authors: Marius E. Yamakou, Tat Dat Tran, Luu Hoang Duc, Juergen Jost
    Abstract:

    In this paper, we provide a complete mathematical construction for a stochastic leaky-integrate-and-fire model (LIF) mimicking the interspike interval (ISI) statistics of a stochastic FitzHugh–Nagumo neuron model (FHN) in the excitable regime, where the unique fixed point is Stable. Under specific types of noises, we prove that there exists a global random attractor for the stochastic FHN system. The linearization method is then applied to estimate the firing time and to derive the associated radial equation representing a LIF equation. This result confirms the previous prediction in Ditlevsen and Greenwood (J Math Biol 67(2):239–259, 2013) for the Morris-Lecar neuron model in the bistability regime consisting of a Stable fixed point and a Stable Limit Cycle.

  • stochastic fitzhugh nagumo neuron model in excitable regime embeds a leaky integrate and fire model
    arXiv: Dynamical Systems, 2018
    Co-Authors: Marius E. Yamakou, Tat Dat Tran, Luu Hoang Duc, Juergen Jost
    Abstract:

    In this paper, we provide a complete mathematical construction for a stochastic leaky-integrate-and-fire model (LIF) mimicking the interspike interval (ISI) statistics of a stochastic FitzHugh-Nagumo neuron model (FHN) in the excitable regime, where the unique fixed point is Stable. Under specific types of noises, we prove that there exists a global random attractor for the stochastic FHN system. The linearization method is then applied to estimate the firing time and to derive the associated radial equation representing a LIF equation. This result confirms the previous prediction in [Ditlevsen, S. and Greenwood, P. (2013). The Morris-Lecar neuron model embeds a leaky integrate-and-fire model. Journal of Mathematical Biology, 67(2):239-259] for the Morris-Lecar neuron model in the bistability regime consisting of a Stable fixed point and a Stable Limit Cycle.

Boris Gutkin - One of the best experts on this subject based on the ideXlab platform.

  • concomitance of inverse stochastic resonance and stochastic resonance in a minimal biStable spiking neural circuit
    Communications in Nonlinear Science and Numerical Simulation, 2020
    Co-Authors: Amirpasha Zamani, Nikita A Novikov, Boris Gutkin
    Abstract:

    Abstract Stochastic Resonance (SR) is a well-known noise-induced phenomenon widely reported in dynamical systems with a threshold, while Inverse Stochastic Resonance (ISR) is an opposing phenomenon observed in the dynamical systems which exhibit bistability between a Stable node and a Stable Limit Cycle. This study shows a co-occurrence of SR and ISR, in a minimal circuit of synaptically coupled spiking neurons that is designed to show bistability between quiescence and a persistent firing mode. We identify noise, synaptic and intrinsic parameters ranges that allow for ISR. The minimal computational model, is investigated for a range of parameters, and our simulations indicate that the main features of SR, are the direct results of dynamical properties which lead to ISR.

Sai Vinjanampathy - One of the best experts on this subject based on the ideXlab platform.

  • quantum synchronization in nanoscale heat engines
    Physical Review E, 2020
    Co-Authors: Noufal Jaseem, Michal Hajdusek, Vlatko Vedral, Rosario Fazio, L C Kwek, Sai Vinjanampathy
    Abstract:

    Owing to the ubiquity of synchronization in the classical world, it is interesting to study its behavior in quantum systems. Though quantum synchronization has been investigated in many systems, a clear connection to quantum technology applications is lacking. We bridge this gap and show that nanoscale heat engines are a natural platform to study quantum synchronization and always possess a Stable Limit Cycle. Furthermore, we demonstrate an intimate relationship between the power of a coherently driven heat engine and its phase-locking properties by proving that synchronization places an upper bound on the achievable steady-state power of the engine. We also demonstrate that such an engine exhibits finite steady-state power if and only if its synchronization measure is nonzero. Finally, we show that the efficiency of the engine sets a point in terms of the bath temperatures where synchronization vanishes. We link the physical phenomenon of synchronization with the emerging field of quantum thermodynamics by establishing quantum synchronization as a mechanism of Stable phase coherence.