Related papers: Hyperbolic Chaos of Turing Patterns
This study investigates chaotic diffusion in multi-scale turbulence driven by nonlinear wave-particle resonance coupling. Turbulent waves with distinct characteristic wavelengths across scales coherently interact with charged particles when…
We analyse the infinite-dimensional limit of the maximally chaotic dynamical systems that are defined on N-dimensional tori. These hyperbolic systems found successful application in computer algorithms that generate high-quality…
It is shown that the Husimi representations of chaotic eigenstates are strongly correlated along classical trajectories. These correlations extend across the whole system size and, unlike the corresponding eigenfunction correlations in…
We investigate the effect of repeated measurement for quantum dynamics of the suppressed systems which classical counterparts exhibit chaos. The essential feature of such systems is the quantum localization phenomena strongly limiting…
The flow in a Hele-Shaw cell with a time-increasing gap poses a unique shrinking interface problem. When the upper plate of the cell is lifted perpendicularly at a prescribed speed, the exterior less viscous fluid penetrates the interior…
Chaotic pattern dynamics in many experimental systems show structured time averages. We suggest that simple universal boundary effects underly this phenomenon and exemplify them with the Kuramoto-Sivashinsky equation in a finite domain. As…
The transition to turbulence is characterized by an abrupt loss of order and predictability, featuring the intermittent proliferation and decay of localized turbulent structures. En-route to becoming fully turbulent, surprisingly order…
This study investigates transient wave dynamics in Turing pattern formation, focusing on waves emerging from localised disturbances. While the traditional focus of diffusion-driven instability has primarily centred on stationary solutions,…
In this third of a series of four articles, we continue the study of the representations of the hamiltonian dynamical transformations of systems of correlated quantized oscillators. By our use of generalized wave function solutions to…
Excitable media are a generic class of models used to simulate a wide variety of natural systems including cardiac tissue. Propagation of excitation waves in this medium results in the formation of characteristic patterns such as rotating…
When two-dimensional pattern-forming problems are posed on a periodic domain, classical techniques (Lyapunov-Schmidt, equivariant bifurcation theory) give considerable information about what periodic patterns are formed in the transition…
We study a 2-spin quantum Turing architecture, in which discrete local rotations \alpha_m of the Turing head spin alternate with quantum controlled NOT-operations. We show that a single chaotic parameter input \alpha_m leads to a chaotic…
An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential…
We investigate the long-term orbital dynamics of spinless extended bodies in Schwarzschild geometry, and show that periodic deviations from spherical symmetry in the shape of a test body may trigger the onset of chaos. We do this by…
The effect of temporal disorder on systems with up-down Z2 symmetry is studied. In particular, we analyze two well-known families of phase transitions: the Ising and the generalized voter universality classes, and scrutinize the…
On timescales that greatly exceed an orbital period, typical planetary orbits evolve in a stochastic yet stable fashion. On even longer timescales, however, planetary orbits can spontaneously transition from bounded to unbound chaotic…
In this paper, the hyperbolic Anderson equation generated by a time-dependent Gaussian noise is under investigation in two fronts: The solvability and large-$t$ asymptotics. The investigation leads to a necessary and sufficient condition…
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…
We consider the Kirchhoff equation on tori of any dimension and we construct solutions whose Sobolev norms oscillates in a chaotic way on certain long time scales. The chaoticity is encoded in the time between oscillations of the norm,…
We present an extension of the chaos-assisted tunneling mechanism to spatially periodic lattice systems. We demonstrate that driving such lattice systems in an intermediate regime of modulation maps them onto tight-binding Hamiltonians with…