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This paper deals with classes of (de)stabilizing switching signals for switched systems. Most of the available conditions for stability of switched systems are sufficient in nature, and consequently, their violation does not conclude…
The kicked rotator model is an essential paradigm in nonlinear dynamics, helping us understand the emergence of chaos and bifurcations in dynamical systems. In this study, we analyze a two-dimensional kicked rotator model considering a…
We consider a widely used form of models for ship maneuvering, whose nonlinearities entail continuous but nonsmooth second-order modulus terms. For such models bifurcations of straight motion are not amenable to standard center manifold…
Structure of bifurcation diagram in the plane of parameters controlling period-doublings for the system of coupled logistic maps is discussed. The analysis is carried out by computing the charts of dynamical regimes and charts of Lyapunov…
We carry out a complete analytical stability study for the SO(8) symmetric phases in the weakly-interacting two-leg ladder. It is shown that the SO(8) symmetry is robust under generic perturbations. Since there are no fixed points in the…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order…
Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate…
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid…
This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the…
Bicoherence analysis is a well established method for identifying the quadratic nonlinearity of stationary processes. However, it is often applied without checking the basic assumptions of stationarity and convergence. The classic…
Nonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to…
It is well-known that shear flows in a strip or in the half plane are unstable for the incompressible Navier-Stokes equations if the viscosity $\nu$ is small enough, provided the horizontal wave number $\alpha$ lies in a small interval,…
We numerically investigated the quantum-classical transition in rf-SQUID systems coupled to a dissipative environment. It is found that chaos emerges and the degree of chaos, the maximal Lyapunov exponent $\lambda_{m}$, exhibits…
We study in this paper the behavior of a periodically driven nonlinear mechanical system. Bifurcation diagrams are found which locate regions of quasiperiodic, periodic and chaotic behavior within the parameter space of the system. We also…
We investigate the bifurcation phenomena for stochastic systems with multiplicative Gaussian noise, by examining qualitative changes in mean phase portraits. Starting from the Fokker-Planck equation for the probability density function of…
Active nematics exhibit spontaneous flows through a well-known linear instability of the uniformly-aligned quiescent state. Here we show that even a linearly stable uniform state can experience a nonlinear instability, resulting in a…
Recent experiments and simulations have shown that unsteady turbulent flows, before reaching a dynamic equilibrium state, display a universal behaviour. We show that the observed universal non-equilibrium scaling can be explained using a…
There is growing interest in anticipating critical transitions in natural systems, often pursued through statistical detection of early warning signals associated with dynamical bifurcations. In stochastic dynamical systems, such signals…
By integrating 4 lines of thoughts: symmetry breaking originally advanced by Anderson, bifurcation from nonlinear dynamics, Landau's theory of phase transition, and the mechanism of emergent rare events studied by Kramers, we introduce a…