相关论文: Wild oscillations in a nonlinear neuron model with…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
This paper attempts to make feasible the evolutionary emergence of novelty in a supposedly deterministic world which behavior is associated with those of the mathematical dynamical systems. The work was motivated by the observation of…
When an oscillator switches abruptly between different frequencies, there is some ambiguity in deciding how the system should be modelled at the switch. Here we describe two seemingly natural models of a switch in a simple…
We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. The investigation deals with a set of three distinct species that evolve according to the standard rules of mobility,…
First return maps of interspike intervals for biological neurons that generate repetitive bursts of impulses can display stereotyped structures (neuronal signatures). Such structures have been linked to the possibility of multicoding and…
Large sparse circuits of spiking neurons exhibit a balanced state of highly irregular activity under a wide range of conditions. It occurs likewise in sparsely connected random networks that receive excitatory external inputs and recurrent…
We investigate the entrainment of a neuron model exhibiting a chaotic spiking-bursting behavior in response to a weak periodic force. This model exhibits two types of oscillations with different characteristic time scales, namely, long and…
Firing patterns in the central nervous system often exhibit strong temporal irregularity and heterogeneity in their time averaged response properties. Previous studies suggested that these properties are outcome of an intrinsic chaotic…
Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works…
Adapting to regularities of the environment is critical for biological organisms to anticipate events and plan. A prominent example is the circadian rhythm corresponding to the internalization by organisms of the $24$-hour period of the…
Non-reciprocal couplings are frequently found in systems out-of-equilibrium such as neuronal networks. We consider generalized Kuramoto models with non-reciprocal adaptive couplings. The non-reciprocity refers to the type of couplings…
Dynamics of a chaotic spiking neuron model are being studied mathematically and experimentally. The Nonlinear Dynamic State neuron (NDS) is analysed to further understand the model and improve it. Chaos has many interesting properties such…
We study the response of an optical system with the Kerr nonlinearity demonstrating Bloch oscillations to a periodic train of coherent pulses. It has been found out that the intensity of the field excited in the system by pulses resonantly…
Network remodeling, or adaptation, in the presence of periodically driven forcings has hereto remained largely unexplored, despite the fact that a broad class of biological transport networks, e.g. animal vasculature, depends on periodic…
In this work we consider a general non-autonomous hybrid system based on the integrate-and-fire model, widely used as simplified version of neuronal models and other types of excitable systems. Our unique assumption is that the system is…
Intensive computational and theoretical work has led to the development of mutliple mathematical models for bursting in respiratory neurons in the pre-B\"otzinger Complex (pre-B\"otC) of the mammalian brainstem. Nonetheless, these previous…
When a periodic 1D system described by a tight-binding model is uniformly initialized with equal amplitudes at all sites, yet with completely random phases, it evolves into a thermal distribution with no spatial correlations. However, when…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in…
The process by which humans synchronize to a musical beat is believed to occur through error-correction where an individual's estimates of the period and phase of the beat time are iteratively adjusted to align with an external stimuli.…