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We have found a way for penetrating the space of the dynamical systems towards systems of arbitrary dimension exhibiting the nonlinear mixing of a large number of oscillation modes through which extraordinarily complex time evolutions…

We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle induced by the Hopf bifurcation. General relations obtained are applied to the stochastic Lorenz system to show that…

We describe general characteristics of the Hodgkin-Huxley neuron's response to a periodic train of short current pulses with Gaussian noise. The deterministic neuron is bistable for antiresonant frequencies. When the stimuli arrive at the…

We investigate spontaneous critical dynamics of excitatory and inhibitory (EI) sparsely connected populations of spiking leaky integrate-and-fire neurons with conductance-based synapses. We use a bottom-up approach to derive a single neuron…

An electronic circuit device, inspired on the FitzHugh-Nagumo model of neuronal excitability, was constructed and shown to operate with characteristics compatible with those of biological sensory neurons. The nonlinear dynamical model of…

Stochastic quasi-cycles for a two species model of the excitatory-inhibitory type, arranged on a triangular loop, are studied. By increasing the strength of the inter-nodes coupling, one moves the system towards the Hopf bifurcation and the…

Experimental evidence suggests that the computational state of cortical systems change according to behavioral and stimulus context. However, it is still unknown what mechanisms underlie this adaptive processing in cortical circuitry. In…

The sensitivity and frequency selectivity of hearing result from tuned amplification by an active process in the mechanoreceptive hair cells. In most vertebrates the active process stems from the active motility of hair bundles. The…

We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when the sum of the delays reaches a critical…

We propose the first fractal frequency mapping, which in a simple form enables to replicate complex neuronal effects. Unlike the conventional filters, which suppress or amplify the input spectral components according to the filter weights,…

How the brain co-ordinates the actions of distant regions in an efficient manner is an open problem. Many believe that cross-frequency coupling between the amplitude of high frequency local field potential oscillations in one region and the…

In neurosciences, the brain processes information via the firing patterns of connected neurons operating across a spectrum of frequencies. To better understand the effects of these frequencies in the neuron dynamics, we have simulated a…

The coherence resonance (CR) of globally coupled Hodgkin-Huxley neurons is studied. When the neurons are set in the subthreshold regime near the firing threshold, the additive noise induces limit cycles. The coherence of the system is…

This paper investigates the dynamic behavior of a simplified single reed instrument model subject to a stochastic forcing of white noise type when one of its bifurcation parameters (the dimensionless blowing pressure) increases linearly…

When following a sequence - such as reading a text or tracking a user's activity - one can measure how the "dictionary" of distinct elements (types) grows with the number of observations (tokens). When this growth follows a power law, it is…

This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try to classify all…

Understanding cognitive processes in the brain demands sophisticated models capable of replicating neural dynamics at large scales. We present a physiologically inspired speech recognition architecture, compatible and scalable with deep…

We review some properties of dynamical systems with slowly varying parameters, when a parameter is moved through a bifurcation point of the static system. Bifurcations with a single zero eigenvalue may create hysteresis cycles, whose area…

Various classes of neurons alternate between high-frequency discharges and silent intervals. This phenomenon is called burst firing. To analyze burst activity in an insect system, grasshopper auditory receptor neurons were recorded in vivo…

Synaptic plasticity and neuron cross-talk are some of the important key mechanisms underlying formation of dynamic clusters of active neurons. The essence of this study is to model and decipher the mechanism of emergence of a task-specific…