By Roberto Serra
This quantity describes our highbrow direction from the physics of advanced sys tems to the technological know-how of synthetic cognitive platforms. It used to be intriguing to find that a few of the suggestions and techniques which achieve describing the self organizing phenomena of the actual global are correct additionally for comprehend ing cognitive approaches. a number of nonlinear physicists have felt the fascination of such discovery in recent times. during this quantity, we'll restrict our dialogue to man made cognitive platforms, with no trying to version both the cognitive behaviour or the worried constitution of people or animals. at the one hand, such synthetic structures are vital according to se; nonetheless, it may be anticipated that their examine will make clear a few normal ideas that are correct additionally to organic cognitive structures. the most objective of this quantity is to teach that nonlinear dynamical platforms have a number of homes which lead them to quite appealing for achieving a few of the ambitions of man-made intelligence. the keenness which was once pointed out above needs to although be certified via a severe attention of the restrictions of the dynamical platforms technique. figuring out cognitive approaches is a huge medical problem, and the achievements reached to this point let no unmarried solution to declare that it's the in basic terms legitimate one. specifically, the process dependent upon nonlinear dynamical platforms, that's our major subject, remains to be in an early degree of development.
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Fig. 1 shows a geometrical representation of the map. X(i+l) 11---------, A o 1 xli) fig. 1. The triangular map. (After Schuster, 1984) The stability criterion introduced above allows us to state that, for A < 1/2, the origin (x* = 0), which is the only fixed point of the map, is asymptotically stable. This may be immediately verified, as Fig. 2a shows, using a graphical representation of the results of successive iterations starting from an initial condition x(O) f:. O. In this interval of values for A, the origin is asymptotically stable for all possible initial conditions with 0 ~ x(O) ~ 1.
It has been widely studied at a phenomenological level without, however, succeeding to develop a unitary theoretical framework. One may speak of "life game" not only because the choice of the microscopic rule which governs its functioning is inspired by a biological metaphor, but also because, in the two-dimensional array which constitutes the "universe" of this game, not only single cells but also "organisms" are born, grow and die. The latter show unpredictable properties which can not be described at the elementary level which does, however, support them.
47 P. 1 o z Fig. 10. Graphical representation of a linear transformation From this transformation the unit square OMIMM2 (see Fig. e. by lao - /3-y1 Thus, if lao - /3-y1 < 1 the areas contract; they dilatate in the opposite case. Let us now consider a specific example of a two-dimensional map: the socalled "Henon map" (Schuster, 1984). This map may be considered as the result of a refinement of the logistic map, when the model takes into account the fact that the linear term (the generation term) must refer to the preceding time-lapse.