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In this paper, we study the dynamics of a reaction-diffusion Cellular Nonlinear Network (RD-CNN) nodel in which the reaction term is represented by Brusselator cell. We investigate the RD-CNN dynamics by means of describing function method. Comparison with classical results for Brusselator equation is provided. Then we introduce a new RD-CNN model with memristor coupling, for which the edge of chaos regime in the parameter space is determined. Numerical simulations are presented for obtaining dynamic patterns in the RD-CNN model with memristor coupling.
Angela Slavova, and Ronald Tetzlaff. "Edge of chaos in reaction diffusion CNN model." Open Mathematics 15.1 (2017): 21-29. <http://eudml.org/doc/288076>.
@article{AngelaSlavova2017, abstract = {In this paper, we study the dynamics of a reaction-diffusion Cellular Nonlinear Network (RD-CNN) nodel in which the reaction term is represented by Brusselator cell. We investigate the RD-CNN dynamics by means of describing function method. Comparison with classical results for Brusselator equation is provided. Then we introduce a new RD-CNN model with memristor coupling, for which the edge of chaos regime in the parameter space is determined. Numerical simulations are presented for obtaining dynamic patterns in the RD-CNN model with memristor coupling.}, author = {Angela Slavova, Ronald Tetzlaff}, journal = {Open Mathematics}, keywords = {Cellular Nonlinear Networks; Reaction-diffusion Brusselator equation; Memristor; Edge of chaos; cellular nonlinear networks; reaction-diffusion Brusselator equation; memristor; edge of chaos}, language = {eng}, number = {1}, pages = {21-29}, title = {Edge of chaos in reaction diffusion CNN model}, url = {http://eudml.org/doc/288076}, volume = {15}, year = {2017}, }
TY - JOUR AU - Angela Slavova AU - Ronald Tetzlaff TI - Edge of chaos in reaction diffusion CNN model JO - Open Mathematics PY - 2017 VL - 15 IS - 1 SP - 21 EP - 29 AB - In this paper, we study the dynamics of a reaction-diffusion Cellular Nonlinear Network (RD-CNN) nodel in which the reaction term is represented by Brusselator cell. We investigate the RD-CNN dynamics by means of describing function method. Comparison with classical results for Brusselator equation is provided. Then we introduce a new RD-CNN model with memristor coupling, for which the edge of chaos regime in the parameter space is determined. Numerical simulations are presented for obtaining dynamic patterns in the RD-CNN model with memristor coupling. LA - eng KW - Cellular Nonlinear Networks; Reaction-diffusion Brusselator equation; Memristor; Edge of chaos; cellular nonlinear networks; reaction-diffusion Brusselator equation; memristor; edge of chaos UR - http://eudml.org/doc/288076 ER -