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Current questions in ecology revolve around instabilities in the dynamics on spatial networks and particularly the effect of node heterogeneity. We extend the Master Stability Function formalism to inhomogeneous biregular networks having…
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…
Properties of stochastic systems are defined by the noise type and deterministic forces acting on the system. In out-of-equilibrium setups, e.g., for motions under action of L\'evy noises, the existence of the stationary state is not only…
We study stationary distributions in the context of stochastic reaction networks. In particular, we are interested in complex balanced reaction networks and reduction of such networks by assuming a set of species (called non-interacting…
The fixed-point analysis refers to the study of fixed-points that arise in the context of complex systems with many interacting entities. In this expository paper, we describe four levels of fixed-points in mean-field interacting particle…
Non-stationarity of the rate or variance of events is a well-known problem in the description and analysis of time series of events, such as neuronal spike trains. A multiple filter test (MFT) for rate homogeneity has been proposed earlier…
We present a stochastic formalism for signal transduction processes in bacterial two-component system. Using elementary mass action kinetics, the proposed model takes care of signal transduction in terms of phosphotransfer mechanism between…
Posttranslational modification of proteins is key in transmission of signals in cells. Many signaling pathways contain several layers of modification cycles that mediate and change the signal through the pathway. Here, we study a simple…
With the increasing complexity of industrial production systems, accurate fault diagnosis is essential to ensure safe and efficient system operation. However, due to changes in production demands, dynamic process adjustments, and complex…
Stochastic resonance is a well established phenomenon, which proves relevant for a wide range of applications, of broad trans-disciplinary breath. Consider a one dimensional bistable stochastic system, characterized by a deterministic…
Many biochemical processes can successfully be described by dynamical systems allowing some form of switching when, depending on their initial conditions, solutions of the dynamical system end up in different regions of state space…
A system containing a pre-steady state standard (non-autocatalytic) reaction, with multiple paths, evolves toward a kinetic state with the minimum attainable activation free energy. Displacement of the path frequency distribution in this…
The streaming instability provides an efficient way of overcoming the growth barriers in the initial stages of the planet formation process. Considering the realistic case of a particle size distribution, the dynamics of the system is…
We study stochastic particle systems that conserve the particle density and exhibit a condensation transition due to particle interactions. We restrict our analysis to spatially homogeneous systems on finite lattices with stationary product…
We study the dynamics of a Josephson junction connected to a dc current supply via a distributed parameter capacitor, which serves as a resonator. We reveal multistability in the current-voltage characteristic of the system; this…
Flow and Diffusion Distributed Structures (FDS) are stationary spatially periodic patterns that can be observed in reaction-diffusion-advection systems. These structures arise when the flow rate exceeds a certain bifurcation point provided…
This paper derives distributed conditions that guarantee the system-wide stability for power systems with nonlinear and heterogeneous bus dynamics interconnected via power network. Our conditions require each bus dynamics should satisfy…
We establish necessary and sufficient conditions for the existence of factorizable steady states of the Generalized Zero Range Process. This process allows transitions from a site $i$ to a site $i+q$ involving multiple particles with rates…
The steady-state degree of a chemical reaction network is the number of complex steady-states for generic rate constants and initial conditions. One way to bound the steady-state degree is through the mixed volume of the steady-state system…
We study analytically and numerically a bistable reaction-diffusion equation on an arbitrary finite network. We prove that stable fixed points (multi-fronts) exist for any configuration as long as the diffusion is small. We also study fold…