Related papers: Attractors in complex networks
Attractor neural network models of cortical decision-making circuits represent them as dynamical systems in the state space of neural firing rates with the attractors of the network encoding possible decisions. While the attractors of these…
This paper provides global attractivity results for the interior equilibrium point of a general Lotka-Volterra system with no restriction on the dimension of the system and with no special structure or properties of the interaction matrix.…
In the first part of this paper, we showed that three coupled populations of identical phase oscillators give rise to heteroclinic cycles between invariant sets where populations show distinct frequencies. Here, we now give explicit…
The basin of attraction is the set of initial points that will eventually converge to some attracting set. Its knowledge is important in understanding the dynamical behavior of a given dynamical system of interest. In this work, we address…
We show that the core reasons that complex and hypercomplex valued neural networks offer improvements over their real-valued counterparts is the weight sharing mechanism and treating multidimensional data as a single entity. Their algebra…
Kernel-based learning methods can dramatically increase the storage capacity of Hopfield networks, yet the dynamical mechanisms behind this enhancement remain poorly understood. We address this gap by combining a geometric characterization…
We use entropy theory as a new tool for studying Lorenz-like classes of flows in any dimension. More precisely, we show that every Lorenz-like class is entropy expansive, and has positive entropy which varies continuously with vector…
We model a social-encounter network where linked nodes match for reproduction in a manner depending probabilistically on each node`s attractiveness. The developed model reveals that increasing either the network`s mean degree or the…
Predators often consume multiple prey and by mutually subsidizing a shared predator, the prey may reciprocally harm each other. When predation levels are high, this apparent competition can culminate in a prey species being displaced.…
Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For…
We study the dynamics of the generalized Lotka-Volterra model with a network structure. Performing a high connectivity expansion for graphs, we write down a mean-field dynamical theory that incorporates degree heterogeneity. This allows us…
In systems biology, attractor landscape analysis of gene regulatory networks is recognized as a powerful computational tool for studying various cellular states from proliferation and differentiation to senescence and apoptosis. Therefore,…
We explicitly construct global attractors of fully nonlinear parabolic equations. The attractors are decomposed as equilibria (time independent solutions) and heteroclinic orbits (solutions that converge to distinct equilibria backwards and…
The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…
Latent Euclidean embedding models a given network by representing each node in a Euclidean space, where the probability of two nodes sharing an edge is a function of the distances between the nodes. This implies that for two nodes to share…
Many neural nets appear to represent data as linear combinations of "feature vectors." Algorithms for discovering these vectors have seen impressive recent success. However, we argue that this success is incomplete without an understanding…
Dynamical systems containing heteroclinic cycles and networks can be invoked as models of intransitive competition between three or more species. When populations are assumed to be well-mixed, a system of ordinary differential equations…
We present an example of a new strange attractor which, as we show, belongs to a class of wild pseudohyperbolic spiral attractors. We find this attractor in a four-dimensional system of differential equations which can be represented as an…
This article discusses a latent variable model for inference and prediction of symmetric relational data. The model, based on the idea of the eigenvalue decomposition, represents the relationship between two nodes as the weighted…
The Kauffman model describes a particularly simple class of random Boolean networks. Despite the simplicity of the model, it exhibits complex behavior and has been suggested as a model for real world network problems. We introduce a novel…