Cellular and Natural Computing Models and Software Simulation - Systematic Design for Emergence in Cellular Nonlinear Networks - page 19

3.2.3 Reaction-Diffusion Cellular Nonlinear Networks

eaction-diffusion CNNs (D-CNNs) [] were proposed as a particular case of

continuous-time autonomous 1 CNN and are discrete-space models of partial dif-
ferential equations describing the reaction-diffusion physical processes.
From a circuit perspective a D-CNN can be modeled as a collection of multi-
port nonlinear cells. These cells are coupled with their neighboring cells via linear
resistive networks (Fig. 3.2).

Fig. 3.2. The topology of a reaction diffusion cellular neural network. A cell is a m -port de-

scribed by a nonlinear ODE which models a physical reaction. The coupling with neighboring

ing cells is done via resistive grids modeling the physical process of diffusion

Example : The case of a reactiondiffusion cell with von Neumann neighbor-
hood . The cell equation is of the following form:

1 1 1 m 2 3 4 5 1

, & x f ( x , x ,..., x , G ) D x x x x 4 x

1 1 1 1

..

j j j j j j

1 1 m

, & x f ( x , x

2

,..., x , G ) D x x x x 4 x

1 j j 5

1 2 3 4 1

..

m 12 m mmmm m

x & f ( xx x , ,..., , G ) Dxxxx x 4 ,

1 m 1 1 1 m m 2 3 4 5 1

1 n autonomous system has no external inputs. Information processing in such systems

consists in prescribing the initial state of all cells with some pattern to be processed

followed by a dynamic transformation of this pattern until a stopping criterion is met.