Related papers: Dynamic bifurcations: hysteresis, scaling laws and…
This paper investigates the different behaviors of the process equation and parameters of their occurrences. The process equation is a multistable one dimensional map with nonlinear feedback and can show various behaviors such as period…
Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response to both small and large perturbations, leading to the…
Systems of coupled sine circle maps show regimes of spatiotemporally intermittent behaviour with associated scaling exponents which belong to the DP class, as well as regimes of spatially intermittent behaviour (with associated regular…
The bifurcation diagram of a model stochastic differential equation with delayed feedback is presented. We are motivated by recent research on stochastic effects in models of transcriptional gene regulation. We start from the normal form…
In this paper we study the stabilization of rotating waves using time delayed feedback control. It is our aim to put some recent results in a broader context by discussing two different methods to determine the stability of the target…
Real power systems exhibit dynamics that evolve across a wide range of time scales, from very fast to very slow phenomena. Historically, incorporating these wide-ranging dynamics into a single model has been impractical. As a result, power…
This work concerns the dynamics of nonlinear systems that are subjected to delayed self-feedback. Perturbation methods applied to such systems give rise to slow flows which characteristically contain delayed variables. We consider two…
A variation in the environment of a system, such as the temperature, the concentration of a chemical solution or the appearance of a magnetic field, may lead to a drift in one of the parameters. If the parameter crosses a bifurcation point,…
Oscillation of macroscopic variables is discovered in a metastable state in the Hamiltonian dynamical system of mean field XY model, the duration of which is divergent with the system size. This long-lasting periodic or quasiperiodic…
In this paper we analyze a generic dynamical system with $\mathbb{D}_2$ constructed via a Cayley graph. We study the Hopf bifurcation and find conditions for obtaining a unique branch of periodic solutions. Our main result comes from…
Initially, the logistic map became popular as a simplified model for population growth. In spite of its apparent simplicity, as the population growth-rate is increased the map exhibits a broad range of dynamics, which include bifurcation…
The aim of this work is to investigate the qualitative behaviour of a financial dynamical system which contains a time delay. We investigate the dynamic response of this system of which variables are interest rate, investment demand, price…
A family of periodic perturbations of an attracting robust heteroclinic cycle defined on the two-sphere is studied by reducing the analysis to that of a one-parameter family of maps on a circle. The set of zeros of the family forms a…
We introduce a versatile class of prototype dynamical systems for the study of complex bifurcation cascades of limit cycles, including bifurcations breaking spontaneously a symmetry of the system, period doubling bifurcations and…
In this paper we introduce a new bifurcation in Hamiltonian systems, which we call the double flip bifurcation. The Hamiltonian depends on two parameters, one of which controls the double flip bifurcation. The result of the bifurcation is…
A simple electronic circuit with a voltage controlled current source is investigated. The circuit exhibits rich dynamics upon varying the circuit elements such as L,C and R, and the control factor of the current source. Among several other…
The fundamental mechanism of hysteresis in the quasistatic limit of multi-stable systems is associated with transitions of the system from one local minimum of the potential energy to another. In this scenario, as system parameters are…
We analyze a class of network motifs in which a short, two-node positive feed- back motif is inserted in a three-node negative feedback loop. We demonstrate that such networks can undergo a bifurcation to a state where a stable fixed point…
There exists a variety of physically interesting situations described by continuous maps that are nondifferentiable on some surface in phase space. Such systems exhibit novel types of bifurcations in which multiple coexisting attractors can…
Dynamic hysteresis, viz., delay in switching of a bistable system on account of the finite sweep rate of the drive has been extensively studied in dynamical and thermodynamic systems. Dynamic hysteresis results from slowing of the response…