Related papers: Chaos and stability in a model of inhibitory neuro…
We prove that a topologically generic network (an open and dense set of networks) of three or more inhibitory neurons have periodic behavior with a finite number of limit cycles that persist under small perturbations of the structure of the…
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…
For infinitely large sparse networks of spiking neurons mean field theory shows that a balanced state of highly irregular activity arises under various conditions. Here we analytically investigate the microscopic irregular dynamics in…
We study the dynamical stability of pulse coupled networks of leaky integrate-and-fire neurons against infinitesimal and finite perturbations. In particular, we compare current versus fluctuations driven networks, the former (latter) is…
We propose a discrete time dynamical system (a map) as phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find condition under which this map has an invariant region on the…
We consider stable periodic helixes as a generalization of stable periodic orbits. We see that in the studied class of iterated functions Chaos always arise suddenly. Therefore, we shall study the route from chaos to order rather than the…
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…
We treat $n$-dimensional piecewise-linear continuous maps with two pieces, each of which has exactly one unstable direction, and identify an explicit set of sufficient conditions for the existence of a chaotic attractor. The conditions…
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…
Stable chaos is a generalization of the chaotic behaviour exhibited by cellular automata to continuous-variable systems and it owes its name to an underlying irregular and yet linearly stable dynamics. In this review we discuss analogies…
The present paper points out to a novel scenario for formation of chaotic attractors in a class of models of excitable cell membranes near an Andronov-Hopf bifurcation (AHB). The mechanism underlying chaotic dynamics admits a simple and…
The generalization properties of an attractive network of non monotonic neurons which infers concepts from samples are studied. The macroscopic dynamics for the overlap between the state of the neurons with the concepts, well as the…
Chaotic neural networks have received a great deal of attention these last years. In this paper we establish a precise correspondence between the so-called chaotic iterations and a particular class of artificial neural networks: global…
Biological neural networks can operate in qualitatively distinct dynamical regimes, and transitions between these regimes are thought to underlie changes in computation and behavior. The seminal work of Sompolinsky, Crisanti, and Sommers…
We demonstrate that final-state uncertainty is ubiquitous in multistable systems of coupled neuronal maps, meaning that predicting whether one such system will eventually be chaotic or nonchaotic is often nearly impossible. We propose a…
Three types of orbits are theoretically possible in autonomous Hamiltonian systems with three degrees of freedom: fully chaotic (they only obey the energy integral), partially chaotic (they obey an additional isolating integral besides…
We investigate species-rich mathematical models of ecosystems. While much of the existing literature focuses on the properties of equilibrium fixed points, persistent dynamics (e.g., limit cycles or chaos) have also been observed, both in…
We disclose the generality of the intrinsic mechanisms underlying multistability in reciprocally inhibitory 3-cell circuits composed of simplified, low-dimensional models of oscillatory neurons, as opposed to those of a detailed Hodgkin-…
Previous studies have shown that, in a diverge-merge network with two intermediate links (the DM network), the kinematic wave model always admits stationary solutions under constant boundary conditions, but periodic oscillations can develop…
The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the…