Dynamics of the Zeraoulia-Sprott map revisited
G. Chen, E.V. Kudryashova, N.V. Kuznetsov, G.A. Leonov
TL;DR
This paper analyzes the boundedness of attractors in the Zeraoulia-Sprott map, providing analytical estimates of absorbing sets to address a key open problem in chaos dynamics.
Contribution
It offers the first analytical study of the attractor boundedness for the Zeraoulia-Sprott map, solving an open problem in chaos theory.
Findings
Boundedness of attractors established
Analytical estimates of absorbing sets derived
Addresses open problem in chaos dynamics
Abstract
In the paper "Some Open Problems in Chaos Theory and Dynamics" by Zeraoulia and Sprott, the two-dimensional map (x,y) -> (-ax(1+y^2)^{-1}, x+by) was considered and the problem of analytical study of the boundedness of its attractors was formulated. In the present paper, the boundedness of its attractors is studied, the corresponding analytical estimation of absorbing set is obtained, and thus an answer to the problem is given.
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