Related papers: Dynamics and Synchronization of Complex Neural Net…
In this paper, the synchronization in a hyper-network of coupled dynamical systems is investigated for the first time. An evolving hyper-network model is proposed for better describing some complex systems. A concept of joint degree is…
The cooperative behavior of neurons and neuronal areas associated with the synchronization behavior proves to be a fundamental neural mechanism. In addition, abnormal levels of synchronization have been related to unhealthy neural…
The paper is to study the asymptotic dynamics in nonmonotone comparable almost periodic reaction-diffusion system with Dirichlet boundary condition, which is comparable with uniformly stable strongly order-preserving system. By appealing to…
Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon…
We consider synchronization of coupled dynamical systems when different types of interactions are simultaneously present. We assume that a set of dynamical systems are coupled through the connections of two or more distinct networks (each…
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…
This paper is concerned with the study of synchronization and consensus phenomena in complex networks of diffusively-coupled nodes subject to external disturbances. Specifically, we make use of stochastic Lyapunov functions to provide…
We present an interacting branching model of neural network dynamics, incorporating key biological features such as inhibition with several types of inhibitory interactions. We establish a hierarchy of analytical mean-field approximations…
We revisit the dynamics of a prototypical model of balanced activity in networks of spiking neutrons. A detailed investigation of the thermodynamic limit for fixed density of connections (massive coupling) shows that, when inhibition…
An exact low-dimensional system of mean-field equations for an infinite-size network of pulse coupled integrate-and-fire neurons with a bimodal distribution of an excitability parameter is derived. Bifurcation analysis of these equations…
Modeling the behavior of coupled networks is challenging due to their intricate dynamics. For example in neuroscience, it is of critical importance to understand the relationship between the functional neural processes and anatomical…
We study the dynamics of two symmetrically coupled populations of identical leaky integrate-and-fire neurons characterized by an excitatory coupling. Upon varying the coupling strength, we find symmetry-breaking transitions that lead to the…
The coherence resonance (CR) of globally coupled Hodgkin-Huxley neurons is studied. When the neurons are set in the subthreshold regime near the firing threshold, the additive noise induces limit cycles. The coherence of the system is…
We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…
The dynamical properties of a diluted fully-inhibitory network of pulse-coupled neurons are investigated. Depending on the coupling strength, two different phases can be observed. At low coupling the evolution rapidly converges towards…
We establish global stability for a chemotaxis-growth model with logarithmic sensitivity under dynamic Dirichlet boundary conditions on a 1D domain. We analyze both parabolic-parabolic and parabolic-hyperbolic systems. The key challenge is…
We analyze zero-lag and cluster synchrony of delay-coupled non-smooth dynamical systems by extending the master stability approach, and apply this to networks of adaptive threshold-model neurons. For a homogeneous population of excitatory…
Neural circuits exhibit structured connectivity, including an overrepresentation of reciprocal connections between neuron pairs. Despite important advances, a full understanding of how such partial symmetry in connectivity shapes neural…
In this letter, we study the leader-synchronization problem for a class of partial differential equations with boundary control and in-domain coupling. We describe the problem in an abstract formulation and we specialize it to a network of…
Spatial relations between neurons in the network with time delays play a crucial role in determining dynamics of the system. During the development of the nervous system different types of neurons group together to enable specific functions…