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The sensitivity of a wave field's evolution to small perturbations is of fundamental interest. For chaotic systems, there are two distinct regimes of either exponential or Gaussian overlap decay in time. We develop a semiclassical approach…
We experimentally demonstrate and numerically simulate a new adaptive method to maintain synchronization between coupled nonlinear chaotic oscillators, when the coupling between the systems is unknown and time-varying (e.g., due to…
For piecewise expanding one-dimensional maps without periodic turning points we prove that isolated eigenvalues of small (random) perturbations of these maps are close to isolated eigenvalues of the unperturbed system. (Here ``eigenvalue''…
We investigate the uniform stability properties of discrete-time linear switched systems subject to arbitrary switching, focusing on the "marginally unstable" regime in which the system is not Lyapunov stable but in which trajectories…
Using an isothermal MHD code, we have performed three-dimensional, high-resolution simulations of the Parker instability. The initial equilibrium system is composed of exponentially-decreasing isothermal gas and magnetic field (along the…
The phase ordering properties of lattices of band-chaotic maps coupled diffusively with some coupling strength $g$ are studied in order to determine the limit value $g_e$ beyond which multistability disappears and non-trivial collective…
We examine the modulational and parametric instabilities arising in a non-autonomous, discrete nonlinear Schr{\"o}dinger equation setting. The principal motivation for our study stems from the dynamics of Bose-Einstein condensates trapped…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
In past works, various schemes for adaptive synchronization of chaotic systems have been proposed. The stability of such schemes is central to their utilization. As an example addressing this issue, we consider a recently proposed adaptive…
Coupled Tchebyscheff maps have recently been introduced to explain parameters in the standard model of particle physics, using the stochastic quantisation of Parisi and Wu. This paper studies dynamical properties of these maps, finding…
A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as…
The phase ordering dynamics of coupled chaotic bistable maps on lattices with defects is investigated. The statistical properties of the system are characterized by means of the average normalized size of spatial domains of equivalent spin…
We investigate the evolution of phase space close to complex unstable periodic orbits in two galactic type potentials. They represent characteristic morphological types of disc galaxies, namely barred and normal (non-barred) spiral…
We investigate the spatio-temporal dynamics of coupled chaotic systems with nonlocal interactions, where each element is coupled to its nearest neighbors within a finite range. Depending upon the coupling strength and coupling radius, we…
The pattern dynamics of the one-way coupled logistic lattice which can serve as a phenomenological model for open flow is investigated and shown to be extremely rich. For medium and large coupling strengths, we find spatially periodic,…
We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical…
Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…
We explore the chaotic dynamics of a large one-dimensional lattice of coupled maps with diffusive coupling of varying strength using the covariant Lyapunov vectors (CLVs). Using a lattice of diffusively coupled quadratic maps we quantify…
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…
Digital implementations of chaotic systems often suffer from inherent degradation, limiting their long-term performance and statistical quality. To address this challenge, we propose a novel four-stage synchronized piecewise linear chaotic…