相关论文: Snaking bifurcations of localized patterns on ring…

In some physical and biological swarms, agents effectively move and interact along curved surfaces. The associated constraints and symmetries can affect collective-motion patterns, but little is known about pattern stability in the presence…

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 examine numerically the dynamics of zz correlations in the spin-1/2 isotropic XY chain with random intersite coupling and on-site transverse field that depends linearly on the neighbouring couplings (correlated off-diagonal and diagonal…

By choosing a dynamical system with d different couplings, one can rearrange a system based on the graph with given vertex dependent on the dynamical system elements. The relation between the dynamical elements (coupling) is replaced by a…

The weak coupling instabilities of a two dimensional Fermi system are investigated for the case of a square lattice using a Wilson renormalization group scheme to one loop order. We focus on a situation where the Fermi surface passes…

Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the…

Interactions in natural communities can be highly heterogeneous, with any given species interacting appreciably with only some of the others, a situation commonly represented by sparse interaction networks. We study the consequences of…

We propose a minimal model of predator-swarm interactions which captures many of the essential dynamics observed in nature. Different outcomes are observed depending on the predator strength. For a "weak" predator, the swarm is able to…

The Hubbard model provides a simple framework in which one can study how certain aspects of the electronic structure of strongly interacting systems can be tuned to optimize the superconducting pairing correlations and how these changes…

We determine the distribution of the number of saddle connections on a random translation surface of large genus. More specifically, for genus $g$ tending to infinity, the number of saddle connections with lengths in a given interval…

To identify emerging microscopic structures in low temperature spin glasses, we study self-sustained clusters (SSC) in spin models defined on sparse random graphs. A message-passing algorithm is developed to determine the probability of…

Small lattices of $N$ nearest neighbor coupled excitable FitzHugh-Nagumo systems, with time-delayed coupling are studied, and compared with systems of FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of equilibria in…

Hidden attractors are present in many nonlinear dynamical systems and are not associated with equilibria, making them difficult to locate. Recent studies have demonstrated methods of locating hidden attractors, but the route to these…

We study the behavior of solutions of mutually coupled equations in heterogeneous random graphs. Heterogeneity means that some equations receive many inputs whereas most of the equations are given only with a few connections. Starting from…

Recently, it has been shown that the minimum number of gauge invariant couplings for $B$-field, metric and dilaton at order $\alpha'^3$ is 872. These couplings, in a particular scheme, appear in 55 different structures. In this paper, up to…

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…

A theory of relative species abundance on sparsely-connected networks is presented by investigating the replicator dynamics with symmetric interactions. Sparseness of a network involves difficulty in analyzing the fixed points of the…

In this paper, we investigate saddle-node to saddle separatrix--loops that we term SNICeroclinic bifurcations. They are generic codimension-two bifurcations involving a heteroclinic loop between one non-hyperbolic and one hyperbolic saddle.…

In this work we investigate the spatiotemporal behaviour of lattices of coupled chaotic logistic maps, where the coupling between sites has a nonlinear form. We show that the stable range of the spatiotemporal fixed point state is…

We study localised activity patterns in neural field equations posed on the Euclidean plane; such models are commonly used to describe the coarse-grained activity of large ensembles of cortical neurons in a spatially continuous way. We…