Related papers: Shadowing Lemma and Chaotic Orbit Determination
We present here a new method which applies well ordered symbolic dynamics to find unstable periodic and non-periodic orbits in a chaotic system. The method is simple and efficient and has been successfully applied to a number of different…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…
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…
We study a class of slow-fast Hamiltonian systems with any finite number of degrees of freedom, but with at least one slow one and two fast ones. At $% \epsilon =0$ the slow dynamics is frozen. We assume that the frozen system (i.e. the…
Special subsets of orbits in chaotic systems, e.g. periodic orbits, heteroclinic orbits, closed orbits, can be considered as skeletons or scaffolds upon which the full dynamics of the system is built. In particular, as demonstrated in…
In this paper targetability of chaotic sets with small controls is discussed by virtue of some results of geometric control theory. It is proved that given a chaotic set {\Lambda}, it is possible to steer a orbit in to every final state in…
We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced…
Stellar pulsation is nowadays a widely understood subject. However, there has been no research about the effects of pulsations on the star's orbital dynamics throughout the galaxy. We investigate whether these oscillations can cause chaotic…
Chaos is an active research subject in the fields of science in recent years. it is a complex and an erratic behavior that is possible in very simple systems. in the present day, the chaotic behavior can be observed in experiments. Many…
Studies of dynamical stability (chaotic versus regular motion) in galactic dynamics often rely on static analytical models of the total gravitational potential. Potentials based upon self-consistent N-body simulations offer more realistic…
Chaos reveals a fundamental paradox in the scientific understanding of Complex Systems. Although chaotic models may be mathematically deterministic, they are practically non-determinable due to the finite precision, which is inherent in all…
Context: Seasonal variations and climate stability of a planet are very sensitive to the planet obliquity and its evolution. This is of particular interest for the emergence and sustainability of land-based life, but orbital and rotational…
We introduce the notion of conditional Lipschitz shadowing, which does not aim to shadow every pseudo-orbit, but only those which belong to a certain prescribed set. We establish two types of sufficient conditions under which certain…
This paper studies the relationship between shadowing phenomena and Bohr chaos in dynamical systems. We provide sufficient conditions for Bohr chaos in terms of shadowing. By combining those conditions with the shadowing lemma, we obtain…
We study the regular or chaotic nature of orbits in a 3D potential describing a triaxial galaxy surrounded by a spherical dark halo component. Our numerical calculations show, that the percentage of chaotic orbits decreases exponentially,…
Predictive Feedback Control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive Feedback Control is severely limited because asymptotic convergence speed decreases with…
This paper explores backward error analysis for numerical solutions of ordinary differential equations, particularly focusing on chaotic systems. Three approaches are examined: residual assessment, the method of modified equations, and…
Lai {\it et al.} \cite{Lai:2002} investigate systems with a stable periodic orbit and a coexisting chaotic saddle. They claim that, by adding white Gaussian noise (GN), averages change with an algebraic scaling law above a certain noise…
The gravitational potentials of realistic galaxy models are in general non-integrable, in the sense that they admit orbits that do not have three independent isolating integrals of motion and are therefore chaotic. However, if chaotic…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…