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Large ensembles of stochastically evolving interacting particles describe phenomena in diverse fields including statistical physics, neuroscience, biology, and engineering. In such systems, the infinitesimal evolution of each particle…
Understanding how local perturbations induce the transient dynamics of a network of coupled units is essential to control and operate such systems. Often a perturbation initiated in one unit spreads to other units whose dynamical state they…
In real-world networks the interactions between network elements are inherently time-delayed. These time-delays can not only slow the network but can have a destabilizing effect on the network's dynamics leading to poor performance. The…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its $d$ variables, an infeasible task for systems with practical limited access and composed of many nodes with high…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable and the set of admissible switching signals obeys pre-specified restrictions on switches between the subsystems and dwell times on…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
Various natural and engineered systems, from urban traffic flow to the human brain, can be described by large-scale networked dynamical systems. These systems are similar in being comprised of a large number of microscopic subsystems, each…
Dynamical properties of numerically approximated discrete systems may become inconsistent with those of the corresponding continuous-time system. We present a qualitative analysis of the dynamical properties of two species Lotka-Volterra…
We study spatiotemporal intermittency in a system of coupled sine circle maps. The phase diagram of the system shows parameter regimes where the STI lies in the directed percolation class, as well as regimes which show pure spatial…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…
A detailed analysis of three species-rich ecosystem food webs has shown that they display scale-free distributions of connections. Such graphs of interaction are in fact shared by a number of biological and technological networks, which…
We introduce and solve a general model of dynamic response under external perturbations. This model captures a wide range of systems out of equilibrium including Ising models of physical systems, social opinions, and population genetics.…
This paper deals with transient stability in interconnected micro-grids. The main contribution involves i) robust classification of transient dynamics for different intervals of the micro-grid parameters (synchronization, inertia, and…
Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When…
Differential diffusion is a source of instability in population dynamics systems when species diffuse with different rates. Predator-prey systems show this instability only under certain specific conditions, usually requiring Holling-type…
This paper, we explore the dynamics of threshold networks on undirected signed graphs. Much attention has been dedicated to understanding the convergence and long-term behavior of this model. Yet, an open question persists: How does the…
A stable population network is hard to interrupt without any ecological consequences. A communication blockage between patches may destabilize the populations in the ecological network. This work deals with the construction of a safe cut…
Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian…