By Johan A K Suykens, Joos P L Vandewalle, Mustak E Yalcin
For engineering purposes which are according to nonlinear phenomena, novel details processing platforms require new methodologies and layout ideas. this angle is the foundation of the 3 cornerstones of this publication: mobile neural networks, chaos and synchronization. mobile neural networks and their common computing device implementations supply a well-established platform for processing spatial-temporal styles and wave computing. Multi-scroll circuits are generalizations to the unique Chua's circuit, resulting in chip implementable circuits with more and more advanced attractors. numerous purposes utilize synchronization options for nonlinear structures. a scientific assessment is given for Lur'e representable platforms with worldwide synchronization standards for master-slave and mutual synchronization, strong synchronization, H synchronization, time-delayed platforms and impulsive synchronization.
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Extra info for Cellular Neural Networks, Multi-Scroll Chaos And Synchronization (World Scientific Series on Nonlinear Science)
The penalty factors 7* emphasize the importance of each of the soft synchronization constraints. ,9. 52) with learning rate r;. 53) where re* = [&T A» T ] T ,// e M2". 54) Ak-iXk fceSi(i) with a sphere of influence «Sj(l). „ 1 [ Unxn UnxnJ , ; h i / n 0nxnl L ^™ UnxnJ A periodic boundary condition was imposed for this CLM-CNN model . This method exploits the spatial-temporal behavior of an 1-D CNN in order to obtain better local minima which result after state synchronization. Therefore, CLMs perform a form of wave computing algorithm which is controlled by the state synchronization.
3 families of scroll grid attractors are presented with simple and systematic circuit realizations. 4 multi-scroll hyperchaotic attractors are presented including hyperchaotic n-scroll attractors and n-scroll hypercubes attractors obtained form unidirectionally or diffusively coupled n-scroll attractors. 5, we develop scroll maps from scroll grid attractors. 6 Lur'e representations of the chaotic and hyperchaotic circuits are discussed. 45 46 Cellular Neural Networks, Multi-Scroll Chaos and Synchronization Fig.
13(e) that specifies which CNN cells are in a certain active or inactive state for all time. The state variables of these cells are frozen tofixedvalues and do not change in time. Therefore, the fixed state option offers an inhomogeneous structure for the CNN array. The ACE 16k CNN chips allow this fixed-state map. 13(c). 13(a) has been chosen as Cellular Neural/Nonlinear Networks 41 Fig. 11 (a-f) Competition between autowaves resulting from the chip-internal sources and an autowave resulting from an externally imposed source.
Cellular Neural Networks, Multi-Scroll Chaos And Synchronization (World Scientific Series on Nonlinear Science) by Johan A K Suykens, Joos P L Vandewalle, Mustak E Yalcin