Related papers: Synchronized Dynamics and Nonequilibrium Steady St…
We study finite state random dynamical systems (RDS) and their induced Markov chains (MC) as stochastic models for complex dynamics. The linear representation of deterministic maps in RDS are matrix-valued random variables whose…
We propose to model the dynamics of metabolic networks from a systems biology point of view by four dynamical structure elements: potential function, transverse matrix, degradation matrix, and stochastic force. These four elements are…
We study systems of identical coupled oscillators introducing a distribution of delay times in the coupling. For arbitrary network topologies, we show that the frequency and stability of the fully synchronized states depend only on the mean…
The long time dynamics of large particles trapped in two inhomogeneous turbulent shear flows is studied experimentally. Both flows present a common feature, a shear region that separates two colliding circulations, but with different…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…
Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…
Filyokov and Karpov [Inzhenerno-Fizicheskii Zhurnal 13, 624 (1967)] have proposed a theory of non-equilibrium steady states in direct analogy with the theory of equilibrium states : the principle is to maximize the Shannon entropy…
Living systems often function with regulatory interactions, but the question of how activity, stochasticity and regulations work together for achieving different goals still remains puzzling. We propose a stochastic model of an active…
Stochasticity is introduced to a well studied class of recursively grown graphs: $(u,v)$-flower nets, which have power-law degree distributions as well as small-world properties (when $u=1$). The stochastic variant interpolates between…
The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the…
We study the synchronization of coupled dynamical systems on a variety of networks. The dynamics is governed by a local nonlinear map or flow for each node of the network and couplings connecting different nodes via the links of the…
Cortical neurons emit seemingly erratic trains of action potentials or "spikes," and neural network dynamics emerge from the coordinated spiking activity within neural circuits. These rich dynamics manifest themselves in a variety of…
We study deterministic continuous-time lossy dynamical flow networks with constant exogenous demands, fixed routing, and finite flow and buffer capacities. In the considered model, when the total net flow in a cell ---consisting of the…
Synchronization is a widespread phenomenon in the brain. Despite numerous studies, the specific parameter configurations of the synaptic network structure and learning rules needed to achieve robust and enduring synchronization in neurons…
Physically motivated stochastic dynamics are often used to sample from high-dimensional distributions. However such dynamics often get stuck in specific regions of their state space and mix very slowly to the desired stationary state. This…
In this work we study the dynamics of Kuramoto oscillators on a stochastically evolving network whose evolution is governed by the phases of the individual oscillators and degree distribution. Synchronization is achieved after a threshold…
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…
We study a network of coupled logistic maps whose interactions occur with a certain distribution of delay times. The local dynamics is chaotic in the absence of coupling and thus the network is a paradigm of a complex system. There are two…
Statistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges. Here, we explore statistical properties and frequentist inference in a model that combines a stochastic block model (SBM) for…