Related papers: Routes to chaos in high-dimensional dynamical syst…
The appearance of infinitely-many period-doubling cascades is one of the most prominent features observed in the study of maps depending on a parameter. They are associated with chaotic behavior, since bifurcation diagrams of a map with a…
Stable chaos is a generalization of the chaotic behaviour exhibited by cellular automata to continuous-variable systems and it owes its name to an underlying irregular and yet linearly stable dynamics. In this review we discuss analogies…
We introduce the $\alpha$-Gauss-Logistic map, a new nonlinear dynamics constructed by composing the logistic and $\alpha$-Gauss maps. Explicitly, our model is given by $x_{t+1} = f_L(x_t)x_t^{-\alpha} - \lfloor f_L(x_t)x_t^{-\alpha} \rfloor…
We analyze the origin and properties of the chaotic dynamics of two atomic ensembles in a driven-dissipative experimental setup, where they are collectively damped by a bad cavity mode and incoherently pumped by a Raman laser. Starting from…
Time-independent Hamiltonian flows are viewed as geodesic flows in a curved manifold, so that the onset of chaos hinges on properties of the curvature two-form entering into the Jacobi equation. Attention focuses on ensembles of orbit…
The Takens-Bogdanov bifurcation is a codimension two bifurcation that provides a key to the presence of complex dynamics in many systems of physical interest. When the system is translation-invariant in one spatial dimension with no…
This paper is the forth part of our series of work, is devoted to the analysis on the multiscales and cascade aspects of the statistical theory of isotropic turbulence based on the new Sedov-type solution. In this paper, we use the explicit…
We study the time evolution of perturbations in spatially extended chaotic systems in the presence of quenched disorder. We find that initially random perturbations tend to exponentially localize in space around static pinning centers that…
The sequences, given by a 7D map have been analysed by means of the methods, widely used to detect chaos in the real world in order to test their sensitivity to chaotic features of a non-linear system determined by comparatively high number…
We establish the emergence of chaotic motion in optomechanical systems. Chaos appears at negative detuning for experimentally accessible values of the pump power and other system parameters. We describe the sequence of period doubling…
Chaos associated with bifurcation makes a new science, but the origin and essence of chaos are not yet clear. Based on the well-known logistic map, chaos used to be regarded as intrinsic randomicity of determinate dynamics systems. However,…
We present an experimental study of the Duffing--Holmes oscillator with a double-well potential, implemented as an analog electronic circuit under periodic external forcing. By systematically varying the forcing amplitude and frequency, we…
Using the quantum trajectories approach we study the quantum dynamics of a dissipative chaotic system described by the Zaslavsky map. For strong dissipation the quantum wave function in the phase space collapses onto a compact packet which…
General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal…
We investigate dynamical tunneling in many dimensional systems using a quasi-periodically modulated kicked rotor, and find that the tunneling rate from the torus to the chaotic region is drastically enhanced when the chaotic states become…
A distribution over instances of a sampling problem is said to exhibit transport disorder chaos if perturbing the instance by a small amount of random noise dramatically changes the stationary distribution (in Wasserstein distance). Seeking…
The dynamical behavior of a higher-order cubic Ginzburg-Landau equation is found to include a wide range of scenarios due to the interplay of higher-order physically relevant terms. We find that the competition between the third-order…
Chaotic itinerancy is a frequently observed phenomenon in high-dimensional and nonlinear dynamical systems, and it is characterized by the random transitions among multiple quasi-attractors. Several studies have revealed that chaotic…
Large deviations in chaotic dynamics have potentially significant and dramatic consequences. We study large deviations of series of finite lengths $N$ generated by chaotic maps. The distributions generally display an exponential decay with…
Transition to hyperchaotic regimes in Rayleigh-Benard convection in a square periodicity cell is studied by three-dimensional numerical simulations. By fixing the Prandtl number at P=0.3 and varying the Rayleigh number as a control…