By A. Slavova
Conventional electronic computation equipment have run right into a se rious velocity bottleneck because of their serial nature. to beat this challenge, a brand new computation version, known as Neural Networks, has been proposed, that is in response to a few elements of neurobiology and tailored to built-in circuits. The elevated availability of com puting strength has not just made many new purposes attainable yet has additionally created the need to accomplish cognitive initiatives that are simply performed by way of the human mind. It turn into seen that new kinds of algorithms and/or circuits have been essential to take care of such projects. notion has been sought from the functioning of the hu guy mind, which resulted in the synthetic neural community process. a technique of taking a look at neural networks is to contemplate them to be arrays of nonlinear dynamical platforms that have interaction with one another. This booklet bargains with one type of in the neighborhood coupled neural internet works, known as mobile Neural Networks (CNNs). CNNs have been intro duced in 1988 by way of L. O. Chua and L. Yang [27,28] as a unique classification of data processing structures, which posseses a few of the key fea tures of neural networks (NNs) and which has vital capability purposes in such components as picture processing and development reco gnition. regrettably, the hugely interdisciplinary nature of the learn in CNNs makes it very tough for a newcomer to go into this significant and fasciriating sector of recent science.
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Extra info for Cellular Neural Networks: Dynamics and Modelling
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. > 0, f(x) = ~3 - x. On of the most powerful methods for studying autonomous nonlinear dynamical systems is the theory that is based on a theorem by Hopf.
41) I d is the identity (n x n) matrix . 8), we have three equilibrium points x = 0, x = ±J3. Then the sum of the eigenvalues of J for x = 0 is: n n L Aq = trace( -A - I d ) = L( -aqq q=l - 1). q=l This sum will be negative for aqq > -1. For the state equilibrium point ii = ±J3, the sum of the eigenvalues of J will be the following: n L Aq n = trace(2A - I d ) = L(2aqq - 1). q=l q=l This sum will be negative for aqq < ~. Therefore the intersection for the two cases is the interval -1 < aqq < ~.
4, in this region we have periodic benaviour of our CNN. 75), we will seek them in the form of trigonometrical Fourier series. This allows us to make a numerical construction of the periodic solutions. Then the approximations of the solutions will be the following: N 'Z:: " D(i) nl cosnt X~i) n=l N L . + E(i) nl sinni , D~~cosnt + E~i~sinnt. 76) The iterations will be stopped when the difference IIx(k) - X(k-l) II ::; 8, 8 is a given small number. This algrithm is very useful, because in the calculations we reach to multiplication, raising to the power and addition of the Fourier polynomials, for which it is possible to compose standard software.
Cellular Neural Networks: Dynamics and Modelling by A. Slavova