Related papers: Sensitivity of Wave Field Evolution and Manifold S…
In quantum/wave systems with chaotic classical analogs, wavefunctions evolve in highly complex, yet deterministic ways. A slight perturbation of the system, though, will cause the evolution to diverge from its original behavior increasingly…
The long-term behaviour of dynamic systems can be classified in two different regimes, regular or chaotic, depending on the values of the control parameters, which are kept constant during the time evolution. Starting from slightly…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
Traditionally, Probability theory was dealing with limit theorems where 'limit" means that time tends to infinity. Questions about finite time dynamics (evolution) were always considered as, although important for practical applications,…
A quantum system is described, whose wave function has a complexity which increases exponentially with time. Namely, for any fixed orthonormal basis, the number of components required for an accurate representation of the wave function…
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…
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final…
The gravitational waveforms of a chaotic system will exhibit sensitive dependence on initial conditions. The waveforms of nearby orbits decohere on a timescale fixed by the largest Lyapunov exponent of the orbit. The loss of coherence has…
Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and…
The defining feature of chaos is its hypersensitivity to small perturbations. However, we report a stability of branched flow against large perturbations where the classical trajectories are chaotic, showing that strong perturbations are…
It is shown, that at weakly nonlinear interaction of waves are possible as modes with chaotic dynamics, and with increasing degree of coherence. Conditions are found at which they arise. One of the types of such interaction is decays. The…
Chaotic evolutions exhibit exponential sensitivity to initial conditions. This suggests that even very small perturbations resulting from weak coupling of a quantum chaotic environment to the position of a system whose state is a non-local…
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…
In many real world chaotic systems, the interest is typically in determining when the system will behave in an extreme manner. Flooding and drought, extreme heatwaves, large earthquakes, and large drops in the stock market are examples of…
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…
Empirical observations in marine ecosystems have suggested a balance of biological and advection time scales as a possible explanation of species coexistence. To characterise this scenario, we measure the time to fixation in neutrally…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
Instabilities of equilibrium quantum mechanics are common and well-understood. They are manifested for example in phase transitions, where a quantum system becomes so sensitive to perturbations that a symmetry can be spontaneously broken.…
Spatio-temporally chaotic dynamics of a classical field can be described by means of an infinite hierarchy of its unstable spatio-temporally periodic solutions. The periodic orbit theory yields the global averages characterizing the chaotic…
Spinning compact binaries are shown to be chaotic in the Post-Newtonian expansion of the two body system. Chaos by definition is the extreme sensitivity to initial conditions and a consequent inability to predict the outcome of the…