3 papers
math.DS2024
New Theorem on Chaos Transitions in Second-Order Dynamical Systems with Tikhonov Regularization
Illych Alvarez
This study examines second-order dynamical systems incorporating Tikhonov regularization. It focuses on how nonlinearities induce bifurcations and chaotic dynamics. By using Lyapun…
nlin.CD2024
Extending Chaos Theory: The Role of Nonlinearity in Multiple Mappings
Illych Alvarez
This work redefines the framework of chaos in dynamical systems by extending Devaney's definition to multiple mappings, emphasizing the pivotal role of nonlinearity. We propose a n…
nlin.CD2024
Advancing Chaos Theory: A Set-Valued Perspective on Multiple Mappings with Computational Detection Algorithms
Illych Alvarez, Ivonne Leon, Ivy Peña
This study redefines the analysis of Devaney chaos in multiple mappings from a set-valued perspective and introduces new conditions to characterize their chaotic behavior. As an in…