Dynamics of q deformed Ricker map

Abstract

We apply the deformation scheme to the classical Ricker map and obtain a q-deformed Ricker map, namely, q-Ricker map. The aim of the paper is to investigate the nonlinear dynamics, bifurcation structure, and topological entropy of q-Ricker map. In particular, we show that q-Ricker map proclaims many exciting phenomena that are remarkable in one-dimensional dynamical systems, such as the presence of coexisting attractors, physically non-observable chaos, hydra paradox, bubbling effect, and extinction. We discuss fold and flip bifurcations and further the presence of stochastically stable chaos. Finally, we show that a certain amount of deformation in the system can keep it in equilibrium; however, excessive deformation causes extinction.

Keywords:

• q-deformation
• Ricker map
• bifurcation
• bubbling effect
• hydra effect
• topological entropy

AMS:

• 92D25
• 37C25
• 37B40
• 37C40

Acknowledgements

The authors would like to thank the referees for reviewing the manuscript and providing their comments and suggestions to improve the manuscript. We are grateful to them for their valuable remarks.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

All data generated or analysed during this study are included in this published article.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Notes

1 This q deformation is not the same as the one we discuss in this paper.