Dynamical systems and paradigms for bio-inspired computing
Pezhman Ebrahimzadeh · RWTH Publications (RWTH Aachen) · 2026
A complex system consists of many interacting elements whose dynamics assumes different spatio-temporal scales, examples of which ranges from neural networks in living matter, neuromorphic computing systems mimicking the brain, coupled memristor systems, conservative and dissipative nonlinear dynamical systems, Earth's climate system, economy, psycho-social phenomenon, and power grid networks, to name a few; nonlinear dynamical systems are of particular interest for modeling of biological, physical and computational systems. In nonlinear dynamical systems, attracting states emerge as long-term behaviors, and multiple attractors can coexist for the same set of system parameters. The emergence and multiplicity of attractors is one of the paradigms how neural networks store patterns as associative memory.In this thesis, we analyze the emergent dynamical behavior of systems of coupled excitable elements with inertia, pendula networks, and study the effects of coupling on the collective behavior. The counterintuitive network attractors, the chimera states, are observed as frequency clustering of the pendula into synchronous manifolds. The stability of the chimeras, as well as fixed points, are studied for various network sizes. The minimal system composed of three pendula has been extensively studied where three types of distinct chimera patterns are identified, with their respective areas of existence and multiplicity regions are found. The switching dynamics between attractors in the region of multiplicity, driven by input and noise, are qualitatively examined with the hypothesis that this sequence of switchings may serve a role in neural computation. Finally, we discuss the experimental setup of minimal metronome network and the resulting chimera states. In conclusion, this thesis provide insights into the potential of attractor dynamics and switching behaviors in complex systems, suggesting applications for neural computation and advancing our understanding of emergent patterns.