Related papers: Almost complete and equable heteroclinic networks

Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…

In a graph, we say that two nodes are topologically equivalent if their sets of first neighbors, excluding the two nodes, coincide. We prove that nonlinearly coupled heterogeneous oscillators located on a group of topologically equivalent…

We prove that steady state bifurcations in finite-dimensional dynamical systems that are symmetric with respect to a monoid representation generically occur along an absolutely indecomposable subrepresentation. This is stated as a…

We establish an equivalence between infinitely many asymptotically stable periodic solutions and subsumed homoclinic connections for $N$-dimensional piecewise-linear continuous maps. These features arise as a codimension-three phenomenon.…

Realistic large-scale networks display an heterogeneous distribution of connectivity weights, that might also randomly vary in time. We show that depending on the level of heterogeneity in the connectivity coefficients, different…

Heteroclinic cycles involving two saddle-foci, where the saddle-foci share both invariant manifolds, occur persistently in some symmetric differential equations on the 3-dimensional sphere. We analyse the dynamics around this type of cycle…

This paper introduces a conception that any weighted directed network topology is almost decouplable, which can help to transform the topology into a similar form being composed of uncoupled vertices, and thus reduce the complexity of…

Can the topology of a network that consists of many particles interacting with each other change in complexity when a phase transition occurs? The answer to this question is particularly interesting to understand the nature of phase…

The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network…

This work is a unified study of stable and unstable steady states of 2D active nematic channel flow using the framework of Exact Coherent Structures (ECS). ECS are stationary, periodic, quasiperiodic, or traveling wave solutions of the…

Shunting inhibitory cellular neural networks (SICNNs) with continuous as well as discontinuous external inputs are investigated. The descriptions of homoclinic and heteroclinic motions are provided in the functional sense for the…

We develop the theoretical foundations of a generalized Gromov-Hausdorff distance between functions on networks that has recently been applied to various subfields of topological data analysis and optimal transport. These functional…

This work analyzes the convergence properties of signed networks with nonlinear edge functions. We consider diffusively coupled networks comprised of maximal equilibrium-independent passive (MEIP) dynamics on the nodes, and a general class…

In this paper, we introduce ergodic sets, subsets of nodes of the networks that are dynamically disjoint from the rest of the network (i.e. that can never be reached or left following to the network dynamics). We connect their definition to…

We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…

Understanding the interactions among nodes in a complex network is of great importance, since they disclose how these nodes are cooperatively supporting the functioning of the network. Scientists have developed numerous methods to uncover…

We study a non-linear dynamical system on networks inspired by the pitchfork bifurcation normal form. The system has several interesting interpretations: as an interconnection of several pitchfork systems, a gradient dynamical system and…

Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds.…

While there has been tremendous activity in the area of statistical network inference on graphs, hypergraphs have not enjoyed the same attention, on account of their relative complexity and the lack of tractable statistical models. We…

In this paper we show the relation between robust transitivity and robust ergodicity for conservative diffeomorphisms. In dimension 2 robustly transitive systems are robustly ergodic. For the three dimensional case, we define it almost…