Chaotic Dynamics of a Three-Dimensional Endomorphism in the Vicinity of the Arnold Tongue
Abstract
The objective of this work is to investigate the transition between periodicity and chaos in the vicinity of Arnold tongues, within the framework of a three-dimensional, nonlinear, and noninvertible discrete dynamical system, which is a specific instance of an endomorphism. Arnold tongues, which represent families of resonance regions in the parameter space, are typically associated with the emergence of periodic orbits. As parameters vary and the system exits these regions, chaotic dynamics can emerge, notably through Neimark–Sacker bifurcations or period-doubling cascades. The analysis reveals alternating regimes of stability and chaos, highlighting how complex dynamics can arise at the boundaries of resonance zones in nonlinear systems.
Fields of Study & Subjects
Chaos control and synchronization
Quantum chaos and dynamical systems
Nonlinear Dynamics and Pattern Formation
Publication details
- Journal / source
- International Journal of Bifurcation and Chaos
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 36
- Issue
- 06
- Publication date
- 29 January 2026
- Language
- EN