By Johan A K Suykens, Joos P L Vandewalle, Mustak E Yalcin
For engineering functions which are in response to nonlinear phenomena, novel details processing structures require new methodologies and layout ideas. this angle is the root of the 3 cornerstones of this publication: mobile neural networks, chaos and synchronization. mobile neural networks and their common laptop implementations provide 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. a number of functions utilize synchronization recommendations for nonlinear structures. a scientific assessment is given for Lur'e representable platforms with international synchronization standards for master-slave and mutual synchronization, powerful synchronization, H synchronization, time-delayed platforms and impulsive synchronization.
Read or Download Cellular Neural Networks, Multi-Scroll Chaos And Synchronization (World Scientific Series on Nonlinear Science) PDF
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Extra resources for Cellular Neural Networks, Multi-Scroll Chaos And Synchronization (World Scientific Series on Nonlinear Science)
12(a) shows the obtained result with a full white image as initial condition. The network has two internal spiral wave sources at the left and right of the image. 12(e). 40 Cellular Neural Networks, Multi-Scroll Chaos and Synchronization Fig. 59) corresponding to the initial and input images from (a) and (d), respectively. g. 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.
A heteroclinic orbit between two saddle-focus-type equilibrium points xe\ and xe2 is a trajectory which tends toward xe\ in reverse time and toward xe2 in forward time. The formal establishment of the existence of these special orbits is the most difficult part of the method . 6) is called a Shilnikov system if these special orbits based at saddle-focus-type equilibrium points are present in the dynamics. There are two important aspects in the Shilnikov method: the Poincare map and the Smale horseshoe  (which is a 2D invariant set for the Smale horseshoe map).
In its simplest form the Smale horseshoe map can be written as fs : S —> R2 where S denotes the unit square in R2. Its basic operation is that of contracting S in the ^-direction and expanding in the y-direction, folding this result (leading to the horseshoe shape) and placing it back over S. The basic process of the Shilnikov method is then to show that the Shilnikov map behaves qualitatively the same as the map fs, thereby ensuring the existence of the Smale horseshoe in the map's discrete dynamics and finally horseshoe chaos in the original third-order continuous system .