Related papers: Autonomous Bursting in a Homoclinic System
We developed a powerful computational approach to elaborate on onset mechanisms of deterministic chaos due to complex homoclinic bifurcations in diverse systems. Its core is the reduction of phase space dynamics to symbolic binary…
We report the phenomenon of frequency clustering in a network of Hodgkin-Huxley neurons with spike timing-dependent plasticity. The clustering leads to a splitting of a neural population into a few groups synchronized at different…
We study in this paper the dynamics of quantum nanoelectronic resonant tunneling diodes (RTDs) as excitable neuromorphic spike generators. We disclose the mechanisms by which the RTD creates excitable all-or-nothing spikes and we identify a…
Self-oscillations are the result of an efficient mechanism generating periodic motion from a constant power source. In quantum devices, these oscillations may arise due to the interaction between single electron dynamics and mechanical…
Large ensembles of globally coupled chaotic neural networks undergo a transition to complete synchronization for high coupling intensities. The onset of this fully coherent behavior is preceded by a regime where clusters of networks with…
We investigate the possibility that narrowband oscillations may emerge from completely asynchronous, independent neural firing. We find that a population of asynchronous neurons may produce narrowband oscillations if each neuron fires…
Hair cells of the auditory and vestibular systems display astonishing sensitivity, frequency selectivity, and temporal resolution to external signals. These specialized cells utilize an internal active amplifier to achieve highly sensitive…
We consider a dynamical system, possibly infinite dimensional or non-autonomous, with fast and slow time scales which is oscillatory with high frequencies in the fast directions. We first derive and justify the limit system of the slow…
Currently we routinely develop a complex neuronal network to explain observed but often paradoxical phenomena based upon biological recordings. Here we present a general approach to demonstrate how to mathematically tackle such a complex…
Large networks of sparsely coupled, excitatory and inhibitory cells occur throughout the brain. A striking feature of these networks is that they are chaotic. How does this chaos manifest in the neural code? Specifically, how variable are…
A collective chaotic phase with power law scaling of activity events is observed in a disordered mean field network of purely excitatory leaky integrate-and-fire neurons with short-term synaptic plasticity. The dynamical phase diagram…
Chaotic bursts are observed in a single-mode microchip Nd:YVO$_4$ laser with fiber feedback. The physical characteristic of the instability is a random switching between two different dynamical states, i.e., the noise-driven relaxation…
We show that a cumulative action of noise and delayed feedback on an excitable theta-neuron leads to rather coherent stochastic bursting. An idealized point process, valid if the characteristic time scales in the problem are well-separated,…
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…
Rapid action potential generation --- spiking --- and alternating intervals of spiking and quiescence --- bursting --- are two dynamic patterns observed in neuronal activity. In computational models of neuronal systems, the transition from…
Coherent scattering of light from ultracold atoms involves an exchange of energy and momentum introducing a wealth of non-linear dynamical phenomena. As a prominent example particles can spontaneously form stationary periodic configurations…
We demonstrate experimentally how semiconductor lasers subjected to double optical feedback change the statistics of their chaotic spiking dynamics from Gaussian to long-tail Power Law distributions associated to the emergency of bursting.…
We present an experimental and theoretical study of an unusual bursting mechanism in a two-mode semiconductor laser with single-mode optical injection. By tuning the strength and frequency of the injected light we find a transition from…
Cultures of neurons grown on multi-electrode arrays have become a common experimental preparation for investigating developing neural networks. Experiment and simulation have shown that these developing networks eventually exhibit bursting…
We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…