相关论文: Mixed-mode oscillations in a multiple time scale p…
The folded node is a singularity associated with loss of normal hyperbolicity in systems where mixtures of slow and fast timescales arise due to singular perturbations. Canards are special solutions that reveal a counteractive feature of…
We examine traveling-wave solutions on a regular ring network with one additional long-range link that spans a distance d. The nodes obey the FitzHugh-Nagumo kinetics in the excitable regime. The additional shortcut induces a plethora of…
We solve a model of a qubit strongly coupled to a massive environmental oscillator mode where the qubit backaction is treated exactly. Using a Ginzburg-Landau formalism, we derive an effective action for this well known localization…
In various neurological disorders spatio-temporal excitation patterns constitute examples of excitable behavior emerging from pathological pathways. During migraine, seizure, and stroke an initially localized pathological state can…
The present paper deals with the dynamics of spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model with a time varying cosmological constant $\Lambda$ where $\Lambda$ evolves with the cosmic time (t) through the…
We quantify the effect of Gaussian white noise on fast--slow dynamical systems with one fast and two slow variables, which display mixed-mode oscillations owing to the presence of a folded-node singularity. The stochastic system can be…
We apply lattice Boltzmann methods to study the segregation of binary fluid mixtures under oscillatory shear flow in two dimensions. The algorithm allows to simulate systems whose dynamics is described by the Navier-Stokes and the…
The sliding mode approach is recognized as an efficient tool for treating the chattering behavior in hybrid systems. However, the amplitude of chattering, by its nature, is proportional to magnitude of discontinuous control. A possible…
We demonstrate that the rapidity and robustness of slow contraction in homogenizing and flattening the universe found in simulations in which the initial conditions were restricted to non-perturbative variations described by a single…
Periodically forced, oscillatory fluid flows have been the focus of intense research for decades due to their richness as a nonlinear dynamical system and their relevance to applications in transportation, aeronautics, and energy…
This paper investigates synchronization phenomena in networks of coupled oscillators governed by three-time-scale dynamical systems exhibiting canard dynamics. A mathematical framework has been developed to analyze the synchronization of…
In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents…
We propose another integrate-and-fire model as a single neuron model. We study a globally coupled noisy integrate-and-fire model with inhibitory interaction using the Fokker-Planck equation and the Langevin equation, and find a reentrant…
We investigate evolutional paths of an extended quintessence with a non-minimally coupled phantom scalar field $\psi$ to the Ricci curvature. The dynamical system methods are used to investigate typical regimes of dynamics at the late time.…
We investigate a possibility of realization of structurally stable chaotic dynamics in neural systems. The considered model of interacting neurons consists of a pair of coupled FitzHugh-Nagumo systems, with the parameters being periodically…
We investigate a ring of $N$ FitzHugh--Nagumo elements coupled in \emph{phase-repulsive} fashion and submitted to a (subthreshold) common oscillatory signal and independent Gaussian white noises. This system can be regarded as a reduced…
In this article, we study the FitzHugh-Nagumo $(1,1)$--fast-slow system where the vector fields associated to the slow/fast equations come from the reduction of the Hodgin-Huxley model for the nerve impulse. After deriving dynamical…
The fluidic pinball is a geometrically simple flow configuration with three rotating cylinders on the vertex of an equilateral triangle. Yet, it remains physically rich enough to host a range of interacting frequencies and to allow testing…
Some bouncing models are investigated in the framework of an extended theory of gravity. The extended gravity model is a simple extension of the General Relativity where an additional matter geometry coupling is introduced to account for…
We determine the behavior of an out-of-equilibrium superfluid, composed of a $U(1)$ Goldstone mode coupled to hydrodynamic modes in a M\" uller-Israel-Stewart theory, in expanding backgrounds relevant to heavy ion collision experiments and…