BIFURCATIONS AND COMPLEXITY DYNAMICS OF BURGERS MAP
By
Til Prasad Sarma1 and L. M. Saha2
1Department of Education in Science and Mathematics, NCERT, Sri Aurobindo Marg, New Delhi, India-110016
2IIIMIT, Shiv Nadar University, Gautam Budh Nagar, Uttar Pradesh, India-201314 Email: tpsncert@gmail.com, lmsaha.msf@gmail.com
(Received: October 08, 2023; In format: April 16, 2024; Revised: May 06, 2024; Accepted: June 29, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54208
Abstract
Detailed investigation done on complexity dynamics of Burger’s map, which internally constituted multicomponent type. The map evolves in different states of its parameter spaces described by parameters (a, b). Bifurcation diagrams of the map display complex dynamical evolutionary behaviors. Complex pattern of orbits observed within the periodic windows of its bifurcation diagrams because of presence of complexities within it. Fixed points and their stability criteria obtained through proper stability analysis. Interesting regular, chaotic and quasi-chaotic attractors drawn for different sets of values of (a,b). Lyapunov exponents, (LCEs), calculated for attractors showing, LCE < 0 for regular case and LCE > 0 for chaotic case. As the system show complexity during evolution, topological entropies calculated assuming it as a measure of complexity. Zero measure of topological entropy obtained in this case, suggests more explanation on complexity. Correlation dimensions are calculated as dimensionality of chaotic attractor. The results obtained demonstrated through interesting graphics. Finally, the Pulsive Feedback Technique applied to regularize the chaotic evolution in Burger’s map.
2020 Mathematical Sciences Classification: 34D45, 37H15, 34C23, 65P20
Keywords: Chaos, Lyapunov Exponents, Bifurcation, Topological Entropy.