Related papers: Stability in simple heteroclinic networks in $\mat…
We investigate the stability properties of two different classes of metabolic cycles using a combination of analytical and computational methods. Using principles from structural kinetic modeling (SKM), we show that the stability of…
We investigate stability of a new class of heteroclinic cycles that we call heteroclinic cycles of type Y. The cycles can be regarded as a generalisation of heteroclinic cycles of type Z introduced in [Podvigina, Nonlinearity 25, 2012]. The…
We address the question how a given connection structure (directed graph) can be realised as a heteroclinic network that is complete in the sense that it contains all unstable manifolds of its equilibria. For a directed graph consisting of…
We study the dynamics near heteroclinic networks for which all eigenvalues of the linearization at the equilibria are real. A common connection and an assumption on the geometry of its incoming and outgoing directions exclude even the…
The concept of stability has a long history in the field of dynamical systems: stable invariant objects are the ones that would be expected to be observed in experiments and numerical simulations. Heteroclinic networks are invariant objects…
In this paper, we investigate stable matching in structured networks. Consider case of matching in social networks where candidates are not fully connected. A candidate on one side of the market gets acquaintance with which one on the…
The paper presents a complete study of simple homoclinic cycles in R^5. We find all symmetry groups Gamma such that a Gamma-equivariant dynamical system in R^5 can possess a simple homoclinic cycle. We introduce a classification of simple…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in…
We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
Interconnected networks describe the dynamics of important systems in a wide range such as biological systems and electrical power grids. Some important features of these systems were successfully studied and understood through simplified…
We analyze the stability of the network's giant connected component under impact of adverse events, which we model through the link percolation. Specifically, we quantify the extent to which the largest connected component of a network…
Stars and cycles are basic structures in network construction. The former has been well studied in network analysis, while the latter attracted rare attention. A node together with its neighbors constitute a neighborhood star-structure…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
Dynamical systems that are invariant under the action of a non-trivial symmetry group can possess structurally stable heteroclinic cycles. In this paper we study stability properties of a class of structurally stable heteroclinic cycles in…
In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge represents either down- or up-regulation, and is modeled by…
Stability is an important characteristic of network models that has implications for other desirable aspects such as controllability. The stability of a Boolean network depends on various factors, such as the topology of its wiring diagram…
We study pseudo-simple heteroclinic cycles for a $\Gamma$-equivariant system in $R^4$ with finite $\Gamma\subset O(4)$, and their nearby dynamics. In particular, in a first step towards a full classification - analogous to that which exists…
The abundance of data about social relationships allows the human behavior to be analyzed as any other natural phenomenon. Here we focus on balance theory, stating that social actors tend to avoid establishing cycles with an odd number of…