Related papers: Feigenbaum scenario without parameters
We study the effect of external stochastic modulation on a system with O(2) symmetry that exhibits a Hopf or oscillatory instability in the absence of modulation. The study includes a random component in both the control parameter of the…
In this paper, we derive analytic expressions for coefficients of the equations that allow calculations of asymptotically periodic points in fractional difference maps. Numerical solution of these equations allows us to draw the bifurcation…
The dynamical phase transition of a system with two coexisting competing order parameters is studied using the time-dependent-Ginzburg-Landau framework. The dynamics are induced by parameters capturing the physics of driving the system with…
Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity…
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…
We study a class of bifurcations generically occurring in dynamical systems with non-mutual couplings ranging from models of coupled neurons to predator-prey systems and non-linear oscillators. In these bifurcations, extended attractors…
Distinguishing long-memory behaviour from nonstationarity is challenging, as both produce slowly decaying sample autocovariances. Existing stationarity tests either fail to account for long-memory processes or exhibit poor empirical size,…
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,…
The stationary and highly non-stationary resonant dynamics of the harmonically forced pendulum are described in the framework of a semi-inverse procedure combined with the Limiting Phase Trajectory concept. This procedure, implying only…
Spin masers are a prototype nonlinear dynamic system. They undergo a bifurcation at a critical amplification factor, transiting into a limit cycle phase characterized by a Larmor precession around the external bias magnetic field, thereby…
We explore different families of quasi-periodically Forced Logistic Maps for the existence of universality and self-similarity properties. In the bifurcation diagram of the Logistic Map it is well known that there exist parameter values…
By considering a solvable driven-dissipative quantum model, we demonstrate that continuous second order phase transitions in dissipative systems may occur without an accompanying spontaneous symmetry breaking. As such, the underlying…
Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the…
The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary…
The regular and chaotic behavior of modified Rayleigh-Duffing oscillator is studied. We consider in this paper the dynamics of Modified Rayleigh Duffing oscillator. The harmonic balance method are used to find the amplitudes of the…
We investigate pattern formation in self-oscillating systems forced by an external periodic perturbation. Experimental observations and numerical studies of reaction-diffusion systems and an analysis of an amplitude equation are presented.…
We use a free-energy minimization approach to describe the secular and dynamical instabilities as well as the bifurcations along equilibrium sequences of rotating, self-gravitating fluid systems. Our approach is fully nonlinear and stems…
A novel experimental paradigm and a novel modelling approach are presented to investigate oscillatory human motor performance by means of a key concept from condensed matter physics, namely, thermodynamic state variables. To this end, in…
Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…
Discrete time crystals are related to non-equilibrium dynamics of periodically driven quantum many-body systems where the discrete time translation symmetry of the Hamiltonian is spontaneously broken into another discrete symmetry.…