Paper's Title:

Strong and Fragile Chaos in a New Two-Dimensional Quadratic Piecewise Smooth Map and Its Applications

Author(s):

Abdellah Menasri, Abdelkadir Soudani

Higher National School of Forests, Khenchela,
System Dynamics and Control Laboratory,
Department of Mathematics and Informatics,
Oum El Bouaghi University,
Algeria.
E-mail: menasri.abdellah@ensf.dz

 
ICOSI Laboratory, Department of Mathematics and Informatics,
College of Science and Technology,
Khenchela University, Khenchela 40004,
Algeria.
E-mail: soudaniabdelkadir@yahoo.com

Abstract:

The Henon and Lozi maps are among the most widely used in physics applications due to their ability to generate two chaotic attractors for specific values of their bifurcation parameters. In this study, I propose a new 2D smooth piecewise quadratic map created by merging the two maps. We demonstrate that this map exhibits both strong and fragile chaotic behavior for varying values of the bifurcation parameters a and b. The new map reveals distinct chaotic attractors, displaying both strong and fragile chaos for certain values of these parameters. Consequently, this map produces two chaotic attractors one fragile and the other strong highlighting the rich diversity of dynamic behavior.

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