Related papers: Non-Stationary Chaos
Our main result is that chaos in dimension $n+1$ is a one-dimensional geometrical object embedded in a geometrical object of dimension $n$ which corresponds to a $n$ dimensional object which is either singular or non-singular. Our main…
Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In…
In this paper we investigate a fractional order logistic map and its discrete time dynamics. We show some basic properties of the fractional logistic map and numerically study its period-doubling route to chaos.
A recent quasiclassical description of a tunneling universe model is shown to exhibit chaotic dynamics by an analysis of fractal dimensions in the plane of initial values. This result relies on non-adiabatic features of the quantum…
Numerical computations of bifurcation maps for one dimensional maps show patterns (regular jumps in point density) in the zones of chaotic behaviour. In this work, empiric formulas are given for these patterns for an entire class of maps.
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…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a new time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the frame of statistical ensemble of quantum…
Piecewise-linear maps describe dynamical phenomena that switch between distinct states and readily generate complex bifurcation structures due to their strong nonlinearity. We show that two-dimensional continuous piecewise-linear maps near…
Nonlinear dynamical systems, ranging from insect populations to lasers and chemical reactions, might exhibit sensitivity to small perturbations in their control parameters, resulting in uncertainties on the predictability of tunning…
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…
Fluctuation-dominated phase ordering refers to a steady state in which the magnitude of long-range order varies strongly owing to fluctuations, and to the associated coarsening phenomena during the approach to steady state. Strong…
Chaotic dynamics is always characterized by swarms of unstable trajectories, unpredictable individually, and thus generally studied statistically. It is often the case that such phase-space densities relax exponentially fast to a limiting…
Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…
Chaotic behavior can be produced from difference equations with unstable fixed points. Difference equations can be used for algorithms to control the chaotic behavior by perturbing a system parameter using feedback based on the first…
A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from that of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace…
We introduce aspects of quantum chaos by analyzing the eigenvalues and the eigenstates of quantum many-body systems. The properties of quantum systems whose classical counterparts are chaotic differ from those whose classical counterparts…
Nonlinear dynamical systems subjected to a combination of noise and time-varying forcing can exhibit sudden changes, critical transitions or tipping points where large or rapid dynamic effects arise from changes in a parameter that are…
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…
We consider infinite harmonic chain with completely deterministic dynamics. Initial data are assumed absolutely bounded. Nevertheless maximum of the variables can grow infinitely in time. We give conditions for this phenomenon. It coincides…