The focus of this thesis is to theoretically and experimentally investigate two new schemes of synchronizing chaotic attractors using chaotically operating diode resonators. The first method, called synchronization using control, is shown for the first time to experimentally synchronize dynamical systems. This method is an economical scheme which can be viably applied to low dimensional dynamical systems. The other, unidirectional coupling, is a straightforward means of synchronization which can be implemented in fast dynamical systems where timing is critical. Techniques developed in this work are of fundamental importance for future problems regarding high dimensional chaotic dynamical systems or arrays of mutually linked chaotically operating elements.
I present a time synchronization algorithm for wireless sensor networks that aims to conserve sensor battery power. The proposed method creates a hierarchical tree by flooding the sensor network from a designated source point. It then uses a hybrid algorithm derived from the timing-sync protocol for sensor networks (TSPN) and the reference broadcast synchronization method (RBS) to periodically synchronize sensor clocks by minimizing energy consumption. In multi-hop ad-hoc networks, a depleted sensor will drop information from all other sensors that route data through it, decreasing the physical area being monitored by the network. The proposed method uses several techniques and thresholds to maintain network connectivity. A new root sensor is chosen when the current one's battery power decreases to a designated value. I implement this new synchronization technique using Matlab and show that it can provide significant power savings over both TPSN and RBS.
The dynamical origin of complexity is an object of intense debate and, up to moment of writing this manuscript, no unified approach exists as to how it should be properly addressed. This research work adopts the perspective of complexity as characterized by the emergence of non-Poisson renewal processes. In particular I introduce two new complex system models, namely the two-state stochastic clocks and the integrate-and-fire stochastic neurons, and investigate its coupled dynamics in different network topologies. Based on the foundations of renewal theory, I show how complexity, as manifested by the occurrence of non-exponential distribution of events, emerges from the interaction of the units of the system. Conclusion is made on the work's applicability to explaining the dynamics of blinking nanocrystals, neuron interaction in the human brain, and synchronization processes in complex networks.
Article describes how the transdisciplinary nature of science as a whole became evident as the necessity for the complex nature of phenomena to explain social and life science, along with the physical sciences, blossomed into complexity theory and most recently into complexitysynchronization. The authors use the scaling of empirical datasets from the brain, cardiovascular and respiratory networks to support the hypothesis that complexity synchronization occurs between scaling indices or equivalently with the matching of the time dependencies of the networks' multifractal dimensions.
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