Cellular Neural Networks: Dynamics and Modelling by A. Slavova

By A. Slavova

Traditional electronic computation tools have run right into a se­ rious velocity bottleneck as a result of their serial nature. to beat this challenge, a brand new computation version, referred to as Neural Networks, has been proposed, that is in accordance with a few points of neurobiology and tailored to built-in circuits. The elevated availability of com­ puting energy has not just made many new functions attainable yet has additionally created the need to accomplish cognitive projects that are simply performed through the human mind. It turn into noticeable that new sorts of algorithms and/or circuits have been essential to deal with such projects. suggestion has been sought from the functioning of the hu­ guy mind, which resulted in the unreal neural community process. a method of taking a look at neural networks is to think about them to be arrays of nonlinear dynamical structures that engage with one another. This publication bargains with one type of in the neighborhood coupled neural internet­ works, referred to as mobile Neural Networks (CNNs). CNNs have been intro­ duced in 1988 by means of L. O. Chua and L. Yang [27,28] as a unique type of data processing platforms, which posseses many of the key fea­ tures of neural networks (NNs) and which has very important power functions in such parts as snapshot processing and development reco­ gnition. regrettably, the hugely interdisciplinary nature of the study in CNNs makes it very tricky for a newcomer to go into this significant and fasciriating region of contemporary technological know-how.

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Additional resources for Cellular Neural Networks: Dynamics and Modelling (Mathematical Modelling: Theory and Applications)

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6 proves that after the transient has decyed to zero in the circuit, CNN always settle at the stable equilibrium states x* and z* given by the following formulas: x* z* £IFl (x*, z*, u*, to), £2F2(X*, z*, «, to). 9 It is easily to prove that the output y(t) = ~ tan -1 ( ~ V z) is a constant after the transient has decayed to zero in the circuit. 10 In reference [27] Chua has been proved that after the transient has decayed to zero CNN settles at the stable equilibrium state if the following condition is satisfied A > 1.

2, b = 1, c = 1, u = 1. All solutions spiral clockwise into the origin with increasing t . Therefore we consider the origin as a stable focus. e. the third case, the phase portrait shows unstable origin. This is because all solutions spiral out clockwise without bounds. For E = 1, a = 0, b = 1, c = 1, u = 1 we have chaotic attractor. In this case we have supercritical Poincare-Andronov-Hopf bifurcation, which has an attracting curve encirling the origin. 78) where al > 1, a2 > 0, bu + i = const.

1. As the first example we shall consider CNN of size 4 x 4. The circuit element par ameters of the cell C( i, j) are chosen as follows. e. 69) 1 < i < 4, 1 ::; j < 4. 0 Observe that all output variab les assume binary values, eit her 1 or -1, as it was poin etd out. 71) IYkL! = 1,1 :S k,l:S 4. 73) can only assume five possible values ; namely, - 4, - 2, 0, 2 and 4. It follows that the corresponding values that can be assumed by the st at e variable Xij are - 6, - 4, ( - 2 or 2), 4, and 6. It follows from the above analysis t hat each inner cell circuit for our present example can have only six possible st able cell equilibrium states ; namely, -6, -4, -2 ,2 ,4 and 6.

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