Related papers: Final state sensitivity and fractal basin boundari…

This work supports the existence of extended nonergodic states in the intermediate region between the chaotic (thermal) and the many-body localized phases. These states are identified through an extensive analysis of static and dynamical…

Self consistent quantum approaches are used to study the instabilities of finite nuclear systems. The frequencies of multipole density fluctuations are determined as a function of dilution and temperature, for several isotopes. The spinodal…

Synaptic interactions structure the phase space of the dynamics of neural circuits and constrain neural computation. Understanding how requires methods that handle those discrete interactions, yet few exist. Recently, it was discovered that…

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…

In this paper we study a two-parameter family of planar maps characterized by two distinct invariant subspaces. The model reveals the existence of two chaotic attractors within these subspaces. We identify parameter values at which these…

Traditional studies of chaos in conservative and driven dissipative systems have established a correspondence between sensitive dependence on initial conditions and fractal basin boundaries, but much less is known about the relation between…

We consider synchronization of chaotic systems coupled indirectly through a common environmnet where the environment has an intrinsic dynmics of its own modulated via feedback from the systems. We find that a rich vareity of synchronization…

Using a system of two FitzHugh-Nagumo units, we demonstrate the occurrence of riddled basins of attraction in delay-coupled systems as the coupling between the units is increased. We characterize the riddled basin using the uncertainty…

We study the emergence of chimera states in a multilayer neuronal network, where one layer is composed of coupled and the other layer of uncoupled neurons. Through the multilayer structure, the layer with coupled neurons acts as the medium…

Synchronization dynamics is a phenomenon of great interest in many fields of science. One of the most important fields is neuron dynamics, as synchronization in certain regions of the brain is related to some of the most common mental…

We study the dynamics of coupled systems, ranging from maps supporting chaotic attractors to nonlinear differential equations yielding limit cycles, under different coupling classes, connectivity ranges and initial states. Our focus is the…

In dynamical systems, basins of attraction connect a given set of initial conditions in phase space to their asymptotic states. The basin entropy and related tools quantify the unpredictability in the final state of a system when there is…

We study the peculiarities of the solitary state appearance in the ensemble of nonlocally coupled chaotic maps. We show that nonlocal coupling and features of the partial elements lead to arising of multistability in the system. The…

The theory of Balanced Neural Networks is a very popular explanation for the high degree of variability and stochasticity in the brain's activity. Roughly speaking, it entails that typical neurons receive many excitatory and inhibitory…

Here we study the emergence of chimera states, a recently reported phenomenon referring to the coexistence of synchronized and unsynchronized dynamical units, in a population of Morris-Lecar neurons which are coupled by both electrical and…

The stability of synchronised networked systems is a multi-faceted challenge for many natural and technological fields, from cardiac and neuronal tissue pacemakers to power grids. In the latter case, the ongoing transition to distributed…

Chaos provides many interesting properties that can be used to achieve computational tasks. Such properties are sensitivity to initial conditions, space filling, control and synchronization. Chaotic neural models have been devised to…

In this work we discuss the most recent results concerning the Vlasov dynamics inside the spinodal region. The chaotic behaviour which follows an initial regular evolution is characterized through the calculation of the fractal dimension of…

We use tools from nonlinear dynamics to the detailed analysis of cold atom experiments. A powerful example is provided by the recent concept of basin entropy which allows to quantify the final state unpredictability that results from the…

We discuss, in this paper, the dynamical properties of extremely diluted, non-monotonic neural networks. Assuming parallel updating and the Hebb prescription for the synaptic connections, a flow equation for the macroscopic overlap is…