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Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of…
Different models of self-excited oscillators which are four-dimensional extensions of the van der Pol system are reported. Their symmetries are analyzed. Three of them were introduced to model the release of vortices behind circular…
Systems of $N$ identical globally coupled phase oscillators can demonstrate a multitude of complex behaviours. Such systems can have chaotic dynamics for $N>4$ when a coupling function is biharmonic. The case $N = 4$ does not possess…
In this article, we explore the possibility of a sub-harmonic $(1{:}2)$ entrainment and supercritical Hopf bifurcation in a van der Pol-Duffing oscillator that has been excited by two frequencies, comprising a slow parametric drive and a…
Systems with the coexistence of different stable attractors are widely exploited in systems biology in order to suitably model the differentiating processes arising in living cells. In order to describe genetic regulatory networks several…
Synchronization is studied in an array of identical oscillators undergoing small vibrations. The overall coupling is described by a pair of matrix-weighted Laplacian matrices; one representing the dissipative, the other the restorative…
We consider suppression of macroscopic synchronized oscillations in mixed populations of active and inactive oscillators with local diffusive coupling, described by a lattice complex Ginzburg-Landau model with discrete Laplacian in general…
Networks of coupled LC oscillators that do not share a common ground node are studied. Both resistive coupling and inductive coupling are considered. For networks under resistive coupling, it is shown that the oscillator-coupler…
Almost all organisms show some kind of time periodicity in their behavior. Especially in mammals the neurons of the suprachiasmatic nucleus form a biological clock regulating the activity-inactivity cycle of the animal. This clock is…
The coexistence of an abnormal rhythm and a normal steady state is often observed in nature (e.g., epilepsy). Such a system is modeled as a bistable oscillator that possesses both a limit cycle and a fixed point. Although bistable…
The Impulsive Goodwin's Oscillator (IGO) is a mathematical model of a hybrid closed-loop system. It arises by closing a special kind of continuous linear positive time-invariant system with impulsive feedback, which employs both amplitude…
The organization of live cells to tissues is associated with the mechanical interaction between cells, which is mediated through their elastic environment. We model cells as spherical active force dipoles surrounded by an infinite elastic…
A system of four coupled oscillators that exhibits unusual synchronization phenomena has been ana- lyzed. Existence of a one-way heteroclinic network, called heteroclinic ratchet, gives rise to uni-directional (de)synchronization between…
We study the changes in the phase portrait of a Van der Pol oscillator in a double well with the change in the shape of the well. Both the symmetric and asymmetric double wells are considered. We find that the shape of the well plays a very…
The oscillatory dynamics of natural and man-made systems can be disrupted by their time-varying interactions, leading to oscillation quenching phenomena in which the oscillations are suppressed. We introduce a framework for analyzing,…
Cyclic motions in vertebrates, including heart beating, breathing and walking, are derived by a network of biological oscillators having fascinating features such as entrainment, environment adaptation, and robustness. These features…
For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all possible two-cluster states and explain how the different states are naturally connected via…
We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips,…
Chemical oscillation is an interesting nonlinear dynamical phenomenon which arises due to complex stability condition of the steady state of a reaction far away from equilibrium which is usually characterised by a periodic attractor or a…
We construct a model of cell reprogramming (the conversion of fully differentiated cells to a state of pluripotency, known as induced pluripotent stem cells, or iPSCs) which builds on key elements of cell biology viz. cell cycles and cell…