Applying the genetic programming to modeling of diffusion processes by using the CNN and its applications to the synchronization

The CNN (Cellular Neural Network) has been proposed as a method of describing the system behavior of neuron coupling with a network structure. This is convenient for analysis of decision risk diffusion in economic society. However, in general, analysis of diffusion becomes possible only after inference of the system dynamics from the observed data. In this paper, using the GP (Genetic Programming) technique, a method is proposed for estimation of dynamics in the CNN. Based on this proposal, the signal diffusion is discussed and a method is proposed for controlling propagation. In order to approximate the system equation in CNN by GP, functions such as piecewise linear ones are prepared in addition to elementary operations. With these and the tree structure containing variables, the individual in the GP is defined. In the GP, two individuals with large degrees of fitness are selected. Crossover processing in the GP is carried out at an appropriately determined place so that an individual with higher capability for approximating the function is generated. In this method, it is shown that approximation is possible, including the system equation of the CNN exhibiting chaotic characteristics. Next, a method of estimating the propagation condition of the signal in CNN by using the estimated system equation is adopted. The results are compared with those derived by simulation and the validity of the computational equation is discussed. In this way, the diffusion coefficient for truncating the signal propagation on the network can be estimated. Further, using the fact that the system equation is available, a control method for synchronization for convergence of the cell state to a stationary point or a limit cycle is proposed. In this method, by means of the measured dynamical results, an appropriate control input in the feedback control can be estimated, allowing control to a balanced level to be attained within a shorter time. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(8): 19–30, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10064