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We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an…
The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent…
We study sustained oscillations in two-dimensional oscillator systems driven by Rayleigh-type negative friction. In particular we investigate the influence of mismatch of the two frequencies. Further we study the influence of external noise…
We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential…
We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…
Dynamical processes on complex networks, ranging from biological, technological and social systems, show phase transitions between distinct global states of the system. Often, such transitions rely upon the interplay between the structure…
Noisy fluctuations are ubiquitous in complex systems. They play a crucial or delicate role in the dynamical evolution of gene regulation, signal transduction, biochemical reactions, among other systems. Therefore, it is essential to…
We investigate dynamics and bifurcations in a mathematical model that captures electrochemical experiments on arrays of microelectrodes. In isolation, each individual microelectrode is described by a one-dimensional unit with a bistable…
In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge represents either down- or up-regulation, and is modeled by…
Chronotaxic systems represent deterministic nonautonomous oscillatory systems which are capable of resisting continuous external perturbations while having a complex time-dependent dynamics. Until their recent introduction in \emph{Phys.…
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…
The inner structure of the attractor appearing when the Varley-Gradwell-Hassell population model bifurcates from regular to chaotic behaviour is studied. By algebraic and geometric arguments the coexistence of a continuum of neutrally…
We consider a model of large regulatory gene expression networks where the thresholds activating the sigmoidal interactions between genes and the signs of these interactions are shuffled randomly. Such an approach allows for a qualitative…
Many complex systems can spontaneously oscillate under non-periodic forcing. Such self-oscillators are commonplace in biological and technological assemblies where temporal periodicity is needed, such as the beating of a human heart or the…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
The ability of a circadian system to entrain to the 24-hour light-dark cycle is one of its most important properties. A new tool, called the entrainment map, was recently introduced to study this process for a single oscillator. Here we…
Non-smooth saddle-node bifurcations give rise to minimal sets of interesting geometry built of so-called strange non-chaotic attractors. We show that certain families of quasiperiodically driven logistic differential equations undergo a…
We investigate bifurcation phenomena between slow and fast convergences of synchronization errors arising in the proposed synchronization system consisting of two identical nonlinear dynamical systems linked by a common noisy input only.…
We describe a new complex system model of an evolving production economy. This model is the simplest we can envisage which incorporates the new observation that the rate of an economic production process depends only on the minimum of its…