| _version_ | 1866901614049099776 |
|---|---|
| author | Revista, Zen MATH, 10 |
| author_facet | Revista, Zen MATH, 10 |
| contents | This paper rigorously investigates the intricate interplay between metastable hyperbolicity and the persistence of transient chaotic behavior within the framework of non-autonomous dynamical systems. While classical hyperbolicity provides a robust foundation for understanding the structural stability of chaotic systems, many real-world phenomena exhibit dynamics that deviate from these strict conditions, often displaying transient chaotic phases before settling into periodic or fixed point attractors, or escaping to infinity. Non-autonomous systems, characterized by explicit time dependence in their governing equations, introduce additional complexities, precluding the existence of classical invariant sets and necessitating novel analytical approaches. We define metastable hyperbolicity as the finite-time manifestation of hyperbolic-like dynamics, where trajectories exhibit exponential divergence and convergence along specific directions for extended durations, without satisfying global uniform hyperbolicity. Our primary objective is to demonstrate how this metastable hyperbolic character provides a robust mechanism for sustaining transient chaos over long, practically significant timescales in non-autonomous contexts. Through theoretical considerations and numerical simulations of representative models, we explore how external forcing or time-varying parameters can continuously re-inject trajectories into regions of metastable hyperbolic saddles, effectively prolonging the chaotic transients. This research offers critical insights into the dynamics of systems where chaos is not a permanent feature but a prolonged, influential transient, challenging traditional distinctions between transient and sustained chaos and extending the understanding of complex behaviors in a wide range of natural and engineered systems. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17809271 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Metastable Hyperbolicity and the Persistence of Transient Chaos in Non-Autonomous Systems Revista, Zen MATH, 10 This paper rigorously investigates the intricate interplay between metastable hyperbolicity and the persistence of transient chaotic behavior within the framework of non-autonomous dynamical systems. While classical hyperbolicity provides a robust foundation for understanding the structural stability of chaotic systems, many real-world phenomena exhibit dynamics that deviate from these strict conditions, often displaying transient chaotic phases before settling into periodic or fixed point attractors, or escaping to infinity. Non-autonomous systems, characterized by explicit time dependence in their governing equations, introduce additional complexities, precluding the existence of classical invariant sets and necessitating novel analytical approaches. We define metastable hyperbolicity as the finite-time manifestation of hyperbolic-like dynamics, where trajectories exhibit exponential divergence and convergence along specific directions for extended durations, without satisfying global uniform hyperbolicity. Our primary objective is to demonstrate how this metastable hyperbolic character provides a robust mechanism for sustaining transient chaos over long, practically significant timescales in non-autonomous contexts. Through theoretical considerations and numerical simulations of representative models, we explore how external forcing or time-varying parameters can continuously re-inject trajectories into regions of metastable hyperbolic saddles, effectively prolonging the chaotic transients. This research offers critical insights into the dynamics of systems where chaos is not a permanent feature but a prolonged, influential transient, challenging traditional distinctions between transient and sustained chaos and extending the understanding of complex behaviors in a wide range of natural and engineered systems. |
| title | Metastable Hyperbolicity and the Persistence of Transient Chaos in Non-Autonomous Systems |
| url | https://doi.org/10.5281/zenodo.17809271 |