By Leon O. Chua

This can be a exact undergraduate point textbook on mobile Nonlinear/neural Networks (CNN) know-how. the numerous examples and excercises, together with a simulator available through the web, make this publication a fantastic advent to CNNs and analogic mobile computing for college kids, researchers and engineers from a variety of backgrounds.

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**Extra resources for Cellular neural networks and visual computing : foundation and applications**

**Sample text**

B) System structure of a center cell C(i, j). Arrow printed in bold denotes the signal fed-back from the outputs of the surround cells. In this case, there are no input signals. 30 Notation, definitions, and mathematical foundation Fig. 24. Uncoupled CNN ∈ C(0, B, z). (a) Signal ﬂow structure of an uncoupled CNN with a 3 × 3 neighborhood. The cone symbolizes the weighted contributions of the input voltages of cells C(k, l) ∈ S1 (i, j) to the center cell C(i, j). (b) System structure of a center cell C(i, j).

2 is called the state dynamic route. The intersection Q of x with the horizontal axis is called an equilibrium point. Observe from the three dynamic routes in Fig. 2 that all trajectories originating from any initial state tend to the equilibrium xi j = xQ . The output yi j can be obtained from the associated output dynamic route y . 4) 1, if wi j ≥ 1 −1, if w ≤ −1 ij Property 2 (Local rule 1) If u i j = −1, then yi j (∞) = −1, independent of u kl ∈ {−1, 1}, k, l ∈ S1 (i, j). 5) ⇒ yi j (∞) = −1.

8) where x = [xˆ1 , xˆ2 , . . , xˆn ]T is the state vector with the same order of state variables. ˆ and Bˆ are n × n matrices whose nonzero entries are the synaptic The two matrices A weights A(i, j; k, l) and B(i, j; k, l), respectively, corresponding to the above three 18 Notation, definitions, and mathematical foundation 0 q q 0 ˆ and B. ˆ Fig. 15. The band structure of A packing schemes. Each matrix is quite sparse (most entries are zero) with the band structure shown in Fig. 15.