Related papers: Oscillations in planar deficiency-one mass-action …
We demonstrate that diffusively coupled limit-cycle oscillators on random networks can exhibit various complex dynamical patterns. Reducing the system to a network analog of the complex Ginzburg-Landau equation, we argue that uniform…
Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which \textit{unstable…
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…
An elementary example shows that the number of zeroes of a component of a solution of a system of linear ordinary differential equations cannot be estimated through the norm of coefficients of the system alone.
We study the effect of intrinsic noise on the thermodynamic balance of complex chemical networks subtending cellular metabolism and gene regulation. A topological network property called deficiency, known to determine the possibility of…
We consider a switched system of two subsystems that are activated as the trajectory enters the regions $\{(x,y):x>\bar x\}$ and $\{(x,y):x<-\bar x\}$ respectively, where $\bar x$ is a positive parameter. We prove that a regular…
The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a…
We study the well-posedness of a class of dynamical flow network systems describing the dynamical mass balance among a finite number of cells exchanging flow of a commodity between themselves and with the external environment. Systems in…
The Social Force Model is one of the most prominent models of pedestrian dynamics. As such naturally much discussion and criticism has spawned around it, some of which concerns the existence of oscillations in the movement of pedestrians.…
We report a transition from asynchronous to oscillatory behaviour in balanced inhibitory networks for class I and II neurons with instantaneous synapses. Collective oscillations emerge for sufficiently connected networks. Their origin is…
We explore the behaviour of chaotic oscillators in hierarchical networks coupled to an external chaotic system whose intrinsic dynamics is dissimilar to the other oscillators in the network. Specifically, each oscillator couples to the…
Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…
From the flashes of fireflies to Josephson junctions and power infrastructure, networks of coupled phase oscillators provide a powerful framework to describe synchronization phenomena in many natural and engineered systems. Most real-world…
We consider stochastically modeled chemical reaction systems with mass-action kinetics and prove that a product-form stationary distribution exists for each closed, irreducible subset of the state space if an analogous deterministically…
In this paper we discuss mechanical systems with inequality constraints. We demonstrate how such constraints can be taken into account by proper modification of the action which describes the original unconstrained dynamics. To illustrate…
In neuroscience, optics and condensed matter there is ample physical evidence for multistable dynamical systems, that is, systems with a large number of attractors. The known mathematical mechanisms that lead to multiple attractors are…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
A model for synchronization of globally coupled phase oscillators including ``inertial'' effects is analyzed. In such a model, both oscillator frequencies and phases evolve in time. Stationary solutions include incoherent (unsynchronized)…
In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the…
Formation control is concerned with the design of control laws that stabilize agents at given distances from each other, with the constraint that an agent's dynamics can depend only on a subset of other agents. When the information flow…