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Biological systems are majorly dependent on their property of bistability in order to exhibit nongenetic heterogeneity in terms of cellular morphology and physiology. Spatial patterns of phenotypically heterogeneous cells, arising due to…
Oscillons are spatially stationary, quasi-periodic solutions of nonlinear field theories seen in settings ranging from granular systems, low temperature condensates and early universe cosmology. We describe a new class of oscillon in which…
Multimode cavity optomechanics, where multiple mechanical degrees of freedom couple to optical cavity modes, provides a rich platform for exploring nonlinear dynamics and engineering complex interactions. In this work, we investigate the…
We demonstrate the mechanisms of emergence and the link between two types of symmetry-broken states, the unbalanced periodic two-cluster states and solitary states, in coupled excitable systems with prevalent repulsive interactions.…
We prove that the famous diffusive Brusselator model can support more complicated spatial-temporal wave structure than the usual temporal-oscillation from a standard Hopf bifurcation. In our investigation, we discover that the diffusion…
Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…
A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…
We examine microscopic mechanisms for coupling stochastic oscillators so that they display similar and correlated temporal variations. Unlike oscillatory motion in deterministic dynamical systems, complete synchronization of stochastic…
We propose a discrete time dynamical system (a map) as phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find condition under which this map has an invariant region on the…
We propose a simple phenomenological model for describing the conformational dynamics of biopolymers via the nonlinearity-induced buckling and collapse (i.e. coiling up) instabilities. Taking into account the coupling between the internal…
This paper attempts to make feasible the evolutionary emergence of novelty in a supposedly deterministic world which behavior is associated with those of the mathematical dynamical systems. The work was motivated by the observation of…
Research on synchronization of coupled oscillators has helped explain how uniform behavior emerges in populations of non-uniform systems. But explaining how uniform populations engage in sustainable non-uniform synchronization may prove to…
We study two models of overdamped self-propelled disks in two dimensions, with and without aligning interactions. Active mesoscale flows leading to chaotic advection emerge in both models in the homogeneous dense fluid away from dynamical…
We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…
The emergence of long-range spatiotemporal order from intrinsic chaos is a central challenge in far-from-equilibrium physics. In active fluids, such as cytoskeletal networks driving cellular motion, self-generated flows typically produce…
We study an abstracted model of neuronal activity via numerical simulation, and report spatiotemporal pattern formation and critical like dynamics. A population of pulse coupled, discretised, relaxation oscillators is simulated over…
We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
We exhibit a resonance mechanism of amplification of density perturbations in inflationary mo-dels, using a minimal set of ingredients (an effective cosmological constant, a scalar field minimally coupled to the gravitational field and…
Super-Bloch oscillations are the outcome of a relative phase between Bloch oscillations and modulations of the periodic lattice. We analyze the dynamics for a model system in which such a relative phase is intrinsically present due to the…
Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…