Related papers: Transitions between spatial attractors in place-ce…

Fluctuational transitions between two co-existing chaotic attractors, separated by a fractal basin boundary, are studied in a discrete dynamical system. It is shown that the mechanism for such transitions is determined by a hierarchy of…

Distributed decision making in multi-agent networks has recently attracted significant research attention thanks to its wide applicability, e.g. in the management and optimization of computer networks, power systems, robotic teams, sensor…

Noise is usually regarded as adversarial to extract the effective dynamics from time series, such that the conventional data-driven approaches usually aim at learning the dynamics by mitigating the noisy effect. However, noise can have a…

Spatially-embedded complex networks, such as nervous systems, the Internet and transportation networks, generally have non-trivial topological patterns of connections combined with nearly minimal wiring costs. However the growth rules…

Living systems, from single cells to higher vertebrates, receive a continuous stream of non-stationary inputs that they sense, e.g., via cell surface receptors or sensory organs. Integrating these time-varying, multi-sensory, and often…

Using an exactly solvable cortical model of a neuronal network, we show that, by increasing the intensity of shot noise (flow of random spikes bombarding neurons), the network undergoes first- and second-order non-equilibrium phase…

We study biased random walkers on lattices with randomly dispersed static traps in one, two and three dimensions. As the external bias is increased from zero the system undergoes a phase transition, most clearly manifested in the asymptotic…

In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to…

Motile eukaryotic cells display distinct modes of migration that often occur within the same cell type. It remains unclear, however, whether transitions between the migratory modes require changes in external conditions, or whether the…

We report an analytic and numerical study of a phase transition in a P problem (the assignment problem) that separates two phases whose representatives are the simple matching problem (an easy P problem) and the traveling salesman problem…

We analyze a class of network motifs in which a short, two-node positive feed- back motif is inserted in a three-node negative feedback loop. We demonstrate that such networks can undergo a bifurcation to a state where a stable fixed point…

We consider a planar dynamical system generated by two stable linear vector fields with distinct fixed points and random switching between them. We characterize singularities of the invariant density in terms of the switching rates and…

Learning navigation capabilities in different environments has long been one of the major challenges in decision-making. In this work, we focus on zero-shot navigation ability using given abstract $2$-D top-down maps. Like human navigation…

The population biology model holds a significant position within ecosystems. Introducing stochastic perturbations into the model can more accurately depict real biological processes. In this paper, we primarily investigate the most probable…

Semiclassical transition probabilities characterize transfer of energy between "hard" and "soft" modes in various physical systems. We establish the boundary problem for singular euclidean solutions used to calculate such probabilities.…

In this paper we give an elementary treatment of the dynamics of skew tent maps. We divide the two-parameter space into six regions. Two of these regions are further subdivided into infinitely many regions. All of the regions are given…

Neural network models comprising elements which have exclusively excitatory or inhibitory synapses are capable of a wide range of dynamic behavior, including chaos. In this paper, a simple excitatory-inhibitory neural pair, which forms the…

We study the effect of competition between short-term synaptic depression and facilitation on the dynamical properties of attractor neural networks, using Monte Carlo simulation and a mean field analysis. Depending on the balance between…

Learning image transformations is essential to the idea of mental simulation as a method of cognitive inference. We take a connectionist modeling approach, using planar neural networks to learn fundamental imagery transformations, like…

Excitable waves arise in many spatially-extended systems of either biological, chemical, or physical nature due to the interplay between local reaction and diffusion processes. Here we demonstrate that similar phenomena are encoded in the…