Related papers: Sensitivity Analysis of Chaotic Systems using Unst…
This paper presents some new criteria for partial exponential stability of a slow-fast nonlinear system with a fast scalar variable using periodic averaging methods. Unlike classical averaging techniques, we construct an averaged system by…
Periodic orbits are among the simplest non-equilibrium solutions to dynamical systems, and they play a significant role in our modern understanding of the rich structures observed in many systems. For example, it is known that embedded…
We analyze the synchronization dynamics of the thermodynamically large systems of globally coupled phase oscillators under Cauchy noise forcings with bimodal distribution of frequencies and asymmetry between two distribution components. The…
In the following we consider a 2-dimensional system of ODE's containing quasiperiodic terms. The system is proposed as an extension of Mathieu-type equations to higher dimensions, with emphasis on how resonance between the internal…
The method of detection of the unstable periodic spatio-temporal states of spatial extended chaotic systems has been proposed. The application of this method is illustrated by the consideration of two different systems: i) the fluid model…
A variational principle for determining unstable periodic orbits of flows as well as unstable spatio-temporally periodic solutions of extended systems is proposed and implemented. An initial loop approximating a periodic solution is evolved…
Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…
We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or…
Chaotic dynamical systems such as turbulent flows are characterized by an exponential divergence of infinitesimal perturbations to initial conditions. Therefore, conventional adjoint/tangent sensitivity analysis methods that are successful…
In a 2D conservative Hamiltonian system there is a formal integral $\Phi$ besides the energy H. This is not convergent near a stable periodic orbit, but it is convergent near an unstable periodic orbit. We explain this difference and we…
In the present work we investigate phase correlations by recourse to the Shannon entropy. Using theoretical arguments we show that the entropy provides an accurate measure of phase correlations in any dynamical system, in particular when…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
In this paper, we implement a generalised pseudo-Newtonian potential to study the off-equatorial orbits inclined at a certain angle with the equatorial plane around Schwarzschild and Kerr-like compact object primaries surrounded by a…
In this contribution, the optimal stabilization problem of periodic orbits is studied via invariant manifold theory and symplectic geometry. The stable manifold theory for the optimal point stabilization case is generalized to the case of…
Many exo-solar systems discovered in the last decade consist of planets orbiting in resonant configurations and consequently, their evolution should show long-term stability. However, due to the mutual planetary interactions a multi-planet…
As originally formulated, the Generalized Alignment Index (GALI) method of chaos detection has so far been applied to distinguish quasiperiodic from chaotic motion in conservative nonlinear dynamical systems. In this paper we extend its…
If you are given a simple three-dimensional autonomous quadratic system that has only one stable equilibrium, what would you predict its dynamics to be, stable or periodic? Will it be surprising if you are shown that such a system is…
Spatiotemporally chaotic dynamics of a Kuramoto-Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as…
We address the issue of how to identify the equations of a largely unknown chaotic system from knowledge about its state evolution. The technique can be applied to the estimation of parameters that drift slowly with time. To accomplish…
Accurate approximations of the change of system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing…