Performance analysis of indicators of chaos for nonlinear dynamical systems
A Bazzani1, M Giovannozzi2, C E Montanari1,2
1Dipartimento di Fisica e Astronomia, Università di Bologna, via Irnerio 46, 40126 Bologna, Italy.
Abstract:
The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed, and new ones have recently been developed in view of improving the performance of chaos detection by means of numerical simulations. The challenge is to predict chaotic behavior based on the analysis of orbits of limited length. In this paper the performance analysis of past and recent indicators of chaos, in terms of predictive power, is carried out in detail using the dynamical system characterized by a symplectic Hénon-like cubic polynomial map.
Related Concept Videos
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
Feedback control systems
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
First Order Systems
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
Second Order systems II
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
Stability
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...


