14 November 2013 New tools for the dynamical description of laser arrays and other complex systems
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We propose a systematic approach that may apply to many complex interactive networks, such as biological or electronic neural assemblies, which was partly inspired by mathematical features of phased laser arrays. Using an appropriate quasi-logarithmic transformation, a Fox-Li integral equation of linearly coupled phased laser arrays is mapped to a semi-equivalent coupled oscillator description, of which the interaction term is decomposed into orthogonal projections. Based on traditional ideas of symmetry, orthogonality, completeness, and the physical concept of criticality, techniques are proposed for the description of the dynamics and organization of massively nonlinearly interconnected networks, which may serve as memories, or perform computational operations in biological neuron assemblies, or models of evolution, pathology, ecological and social networks, individual and collective behavior, etc.
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Erik J. Bochove, Erik J. Bochove, Niketh Nair, Niketh Nair, Alejandro B. Aceves, Alejandro B. Aceves, Mohammad R. Zunoubi, Mohammad R. Zunoubi, "New tools for the dynamical description of laser arrays and other complex systems", Proc. SPIE 8885, Laser-Induced Damage in Optical Materials: 2013, 88851H (14 November 2013); doi: 10.1117/12.2031604; https://doi.org/10.1117/12.2031604

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