Related papers: Phase reduction approach to synchronization of spa…
We consider a class of nonequilibrium systems of interacting agents with pairwise interactions and quenched disorder in the dynamics featuring, in the thermodynamic limit, phase transitions. We provide conditions on the microscopic…
We consider a system of reaction-diffusion equations in a bounded interval of the real line, with emphasis on the metastable dynamics, whereby the time-dependent solution approaches the steady state in an asymptotically exponentially long…
The advent in recent years of highly parallelized microfluidic chemical reaction systems necessitates an understanding of all fluid dynamic time scales including the often neglected millisecond time scale of the inertia of the liquid. We…
We develop a theory to calculate the effective phase diffusion coefficient and the mean phase velocity in periodically driven stochastic models with two discrete states. This theory is applied to a dichotomically driven Markovian two state…
We investigate the synchronization dynamics of two coupled noise-driven FitzHugh-Nagumo systems, representing two neural populations. For certain choices of the noise intensities and coupling strength, we find cooperative stochastic…
Network interactions between dynamical units are often subject to time delay. We develop a phase reduction method for delay-coupled oscillator networks. The method is based on rewriting the delay-differential equation as an ordinary…
A new mathematical model of memristive neural networks described by the partly diffusive reaction-diffusion equations with weak synaptic coupling is proposed and investigated. Under rather general conditions it is proved that there exists…
We develop a formalism to analyze the behaviour of pulse--coupled identical phase oscillators with a specific attention devoted to the onset of partial synchronization. The method, which allows describing the dynamics both at the…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
Given the high dimensionality and underlying complexity of many oscillatory dynamical systems, phase reduction is often an imperative first step in control applications where oscillation timing and entrainment are of interest.…
This work deals with the position control of selected patterns in reaction-diffusion systems. Exemplarily, the Schl\"{o}gl and FitzHugh-Nagumo model are discussed using three different approaches. First, an analytical solution is proposed.…
The universal equations describing collective oscillations of the multidomain patterns of small period in an arbitrary $d$-dimensional reaction-diffusion system of the activator-inhibitor type are asymptotically derived. It is shown that…
The Kuramoto phase diffusion equation is a nonlinear partial differential equation which describes the spatio-temporal evolution of a phase variable in an oscillatory reaction diffusion system. Synchronization manifests itself in a…
The role of dimensionality (Euclidean versus fractal), spatial extent, boundary effects and system topology on the efficiency of diffusion-reaction processes involving two simultaneously-diffusing reactants is analyzed. We present…
Using straightforward linear algebra we derive response operators describing the impact of small perturbations to finite state Markov processes. The results can be used for studying empirically constructed - e.g. from observations or…
Oscillatory chemical reactions often serve as a timing clock of cellular processes in living cells. The temporal dynamics of protein concentration levels is thus of great interest in biology. Here we propose a theoretical framework to…
In this paper, we define the phase response for a class of multi-input multi-output (MIMO) linear time-invariant (LTI) systems whose frequency responses are (semi-)sectorial at all frequencies. The newly defined phase concept subsumes the…
As biochemical systems may frequently suffer from limited energy resources so that internal molecular fluctuation has to be utilized to induce random rhythm, it is still a great theoretical challenge to understand the elementary principles…
Phase field crystal (PFC) models constitute a field theoretical approach to solidification, melting and related phenomena at atomic length and diffusive time scales. One of the advantages of these models is that they naturally contain…
Biochemical networks play a crucial role in biological systems, implementing a broad range of vital functions. They normally operate at low copy numbers and in spatial settings, but this is often ignored and well-stirred conditions are…