On the implementation of the 0–1 test for chaos
GA Gottwald, I Melbourne - SIAM Journal on Applied Dynamical Systems, 2009 - SIAM
In this paper we address practical aspects of the implementation of the 0–1 test for chaos in
deterministic systems. In addition, we present a new formulation of the test which …
deterministic systems. In addition, we present a new formulation of the test which …
The Lyapunov characteristic exponents and their computation
C Skokos - Dynamics of Small Solar System Bodies and …, 2009 - Springer
We present a survey of the theory of the Lyapunov Characteristic Exponents (LCEs) for
dynamical systems, as well as of the numerical techniques developed for the computation of …
dynamical systems, as well as of the numerical techniques developed for the computation of …
[BOOK][B] Extremes and recurrence in dynamical systems
Written by a team of international experts, Extremes and Recurrence in Dynamical Systems
presents a unique point of view on the mathematical theory of extremes and on its …
presents a unique point of view on the mathematical theory of extremes and on its …
Geometrical properties of local dynamics in Hamiltonian systems: The Generalized Alignment Index (GALI) method
We investigate the detailed dynamics of multi-dimensional Hamiltonian systems by studying
the evolution of volume elements formed by unit deviation vectors about their orbits. The …
the evolution of volume elements formed by unit deviation vectors about their orbits. The …
On detecting chaos in a prey-predator model with prey's counter-attack on juvenile predators
B Ghanbari - Chaos, Solitons & Fractals, 2021 - Elsevier
Chaotic nonlinear systems are systems whose main feature is extreme sensitivity to noise in
the problem or the corresponding initial conditions. In this paper, we examine the chaotic …
the problem or the corresponding initial conditions. In this paper, we examine the chaotic …
Analysis and circuit implementation of a non-equilibrium fractional-order chaotic system with hidden multistability and special offset-boosting
S Yan, E Wang, Q Wang - Chaos: An Interdisciplinary Journal of …, 2023 - pubs.aip.org
In order to obtain a system of higher complexity, a new fractional-order chaotic system is
constructed based on the Sprott system. It is noteworthy that the system has no equilibrium …
constructed based on the Sprott system. It is noteworthy that the system has no equilibrium …
Comparative study of variational chaos indicators and ODEs' numerical integrators
The reader can find in the literature a lot of different techniques to study the dynamics of a
given system and also, many suitable numerical integrators to compute them …
given system and also, many suitable numerical integrators to compute them …
Qualitative analysis of the Rössler equations: Bifurcations of limit cycles and chaotic attractors
In this paper we study different aspects of the paradigmatic Rössler model. We perform a
detailed study of the local and global bifurcations of codimension one and two of limit cycles …
detailed study of the local and global bifurcations of codimension one and two of limit cycles …
Lyapunov indices with two nearby trajectories in a curved spacetime
X Wu, TY Huang, H Zhang - Physical Review D—Particles, Fields, Gravitation …, 2006 - APS
We compare three methods for computing invariant Lyapunov exponents (LEs) in general
relativity. These methods involve the geodesic deviation vector technique (M1), the two …
relativity. These methods involve the geodesic deviation vector technique (M1), the two …
Painting chaos: a gallery of sensitivity plots of classical problems
R Barrio - International Journal of Bifurcation and Chaos, 2006 - World Scientific
In this paper we study briefly several chaos indicators and we focus our attention on the
recently developed, presenting a numerical scheme for its calculation based on the Taylor …
recently developed, presenting a numerical scheme for its calculation based on the Taylor …