Abstract
This paper presents new mathematical models of classical (CL) and quantum-mechanical lattices (QML). System—theoretic results on the observability, controllability and minimal realizability theorems are formulated for CL. The cellular dynamaton (CD) based on quantum oscillators is presented. We investigate the conditions when stochastic resonance can occur through the interaction of dynamical neurons with intrinsic deterministic noise and an external periodic control. We found a chaotic motion in phase—space surrounding the separatrix of dynamaton. The suppression of chaos around the hyperbolic saddle arises only for a critical external control field strength and phase. The possibility of the use of bilinear lattice models for simulating the CA3 region of the hippocampus (a common location of the epileptic focus) is discussed. This model consists of a hexagonal CD of nodes, each describing a controlled neural network model consisting of a group of prototypical excitatory pyramidal cells and a group of prototypical inhibitory interneurons connected via excitatory and inhibitory synapses. A nonlinear phenomenon in this neural network is studied.
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Pardalos, P.M., Sackellares, J.C., Yatsenko, V.A. (2002). Classical and Quantum Controlled Lattices: Self-Organization, Optimization and Biomedical Applications. In: Pardalos, P.M., Principe, J. (eds) Biocomputing. Biocomputing, vol 1. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0259-9_12
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DOI: https://doi.org/10.1007/978-1-4613-0259-9_12
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