Basin of attraction

Experimental Definition of the Basin of attraction for Chua's Circuit

Chaos is a dynamic phenomenon that can arise in physical nonlinear systems of very different natures, but nowhere else is it so ubiquitous and easily observed as in electronic circuits [Thompson & Chua, 1995]. We can identify two main reasons for this. First, the simplicity and inexpensive nature of the devices used, and second, the physics of electronic devices is well understood, so that the ...

The basin of attraction of one-dimensional maps

This paper is motivated by a conjecture due to the first author and A. Yakubu [6] concerning the Ricker’s model [10] [4]. It was conjectured that the basin of attraction of an attracting 2-cycle is (0,∞)\E, where E is the set of all eventually 2-periodic points, 0 ≤ r < k [6]. In this paper we prove this conjecture and much more. In fact we prove the same result for continuous maps on compact i...

Basin of attraction determines hysteresis in explosive synchronization.

Spontaneous explosive emergent behavior takes place in heterogeneous networks when the frequencies of the nodes are positively correlated to the node degree. A central feature of such explosive transitions is a hysteretic behavior at the transition to synchronization. We unravel the underlying mechanisms and show that the dynamical origin of the hysteresis is a change of basin of attraction of ...

Perception as a Dynamical Sensori-Motor Attraction Basin

In this paper, we propose a formal definition of the perception as a behavioral dynamical attraction basin. The perception is built from the integration of the sensori-motor flow. Psychological considerations and robotic experiments on an embodied " intelligent " system are provided to show how this definition can satisfy both psychologist and robotician point of view.

Basin of Attraction of Periodic Orbits of Maps on the Real Line