SYNCHRONIZATION OF CHAOS THROUGH UNPREDICTABILITY IN DYNAMICAL SYSTEMS

Date

2024-1-26

Author

Başkan, Kağan

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The investigation of chaos synchronization spans three decades, resulting in the development of several methods such as identical, phase, and generalized synchronization. However, conventional methods often fail to detect synchronized patterns in systems lacking fully unison dynamics. To address this limitation, delta synchronization of Poincaré chaos is introduced, aiming to explain partially synchronized patterns. This novel synchronization type is built upon unpredictability, a concept that reveals chaotic dynamics in systems based on characteristic time sequences—specifically, sequences of convergence and separation. The presence of unpredictability guarantees Poisson stable motion and sensitivity by examining a single trajectory (or single initial condition set) of a system. Numerically, delta synchronization captures the common characteristic time sequences of unpredictability in both coupled and uncoupled systems. This method is applied to various models in this thesis, encompassing distinctive dynamics defined by ordinary, partial, and delay differential equations. In the case of unidirectionally coupled gas-discharge semiconductor systems, the absence of generalized synchronization is noted. For Mackey-Glass delay systems, generalized synchronization occurs only after surpassing a well-known threshold. Importantly, delta synchronization is demonstrated to occur in regions where generalized synchronization is absent for these models. Additionally, the same phenomenon is observed in the uncoupled Hindmarsh-Rose neural network for noise intensity domains where identical synchronization is absent, yet delta synchronization exists. This model is constructed with Markovian noise, and noise-induced synchronization is investigated. In the domains of generalized and identical synchronization, a stronger form of delta synchronization—complete synchronization of unpredictability—is detected.

Subject Keywords

Unpredictability, Delta synchronization, Gas-discharge semiconductor systems, Mackey-Glass systems, Hindmarsh-Rose neural network

URI

https://hdl.handle.net/11511/108356

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Graduate School of Natural and Applied Sciences, Thesis