相关论文: Steady-state bifurcations for three-cell networks …
We construct families of symmetric, antisymmetric, and asymmetric solitary modes in one-dimensional bichromatic lattices with the second-harmonic-generating ($\chi ^{(2)}$) nonlinearity concentrated at a pair of sites placed at distance…
We introduce a dual-core system with double symmetry, one between the cores, and one along each core, imposed by the spatial modulation of local nonlinearity in the form of two tightly localized spots, which may be approximated by a pair of…
Various biological phenomena, like cell differentiation and pattern formation in multicellular organisms, are explained using the bifurcation theory. Molecular network motifs like positive feedback and mutual repressor exhibit bifurcation…
We introduce discrete systems in the form of straight (infinite) and ring-shaped chains, with two symmetrically placed nonlinear sites. The systems can be implemented in nonlinear optics (as waveguiding arrays) and BEC (by means of an…
We study the generic non-equilibrium steady states in asymmetric exclusion processes on a closed network with bottlenecks. To this end we proposes and study closed simple networks with multiply-connected non-identical junctions. Depending…
A coupled cell network describes interacting (coupled) individual systems (cells). As in networks from real applications, coupled cell networks can represent inhomogeneous networks where different types of cells interact with each other in…
The stability of synchronous states is analysed in the context of two populations of inhibitory and excitatory neurons, characterized by different pulse-widths. The problem is reduced to that of determining the eigenvalues of a suitable…
Inter-layer synchronization is a dynamical state occurring in multi-layer networks composed of identical nodes. The state corresponds to have all layers synchronized, with nodes in each layer which do not necessarily evolve in unison. So…
The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling…
The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine…
Homoclinic and heteroclinic connections can form cycles and networks in phase space, which organize global phenomena in dynamical systems. On the one hand, stability notions for (omni)cycles give insight into how many initial conditions…
The dynamics of a multiplex heterogeneous network of oscillators is studied. Two types of similar models based on the Hodgkin-Huxley formalism are used as the basic elements of the networks. The first type model demonstrates bursting…
Synchronization is essential for proper functioning of the power grid. We investigate the synchronous state and its stability for a network with a cyclic topology and with the evolution of the states satisfying the swing equations. We…
The purpose of this paper is trifold -- to serve as an instructive resource and a reference catalog for biologically plausible modeling with i) conductance-based models, coupled with ii) strength-varying slow synapse models, culminating in…
In a previous paper, the authors developed a method for computing normal forms of dynamical systems with a coupled cell network structure. We now apply this theory to one-parameter families of homogeneous feed-forward chains with…
When identical oscillators are coupled together in a network, dynamical steady states are often assumed to reflect network symmetries. Here we show that alternative persistent states may also exist that break the symmetries of the…
We study a simple map as a minimal model of excitable cells. The map has two fast variables which mimic the behavior of class I neurons, undergoing a sub-critical Hopf bifurcation. Adding a third slow variable allows the system to present…
We consider the problem of network coding across three unicast sessions over a directed acyclic graph, where each sender and the receiver is connected to the network via a single edge of unit capacity. We consider a network model in which…
We investigate the nonlinear Schr\"odinger equation on a three-edge star graph, where each edge contains a linear localized inhomogeneity in the form of a Dirac delta linear potential. Such systems are of significant interest in studying…
This paper investigates synchronization phenomena in networks of coupled oscillators governed by three-time-scale dynamical systems exhibiting canard dynamics. A mathematical framework has been developed to analyze the synchronization of…