Modeling Complex Dynamics via Extended PWL-Based CNNs

In this paper a new strategy is proposed in order to extend the class of complex and chaotic dynamics which can be generated by a State-Controlled CNN (SC-CNN). It is shown that, with slight modifications to the original paradigm, it is possible to represent a wide class of nonlinearities by using only piecewise linear (PWL) nonlinearities as output functions of the CNN. The adopted circuitry is presented, together with several examples concerning the emulation of the Rassler and Lorenz chaotic systems, and the Partial Differential Equations (PDE) governing the complex phenomena of solitons (Korteweg–de Vries PDE) and the activator–inhibitor reaction for the formation of patterns in the sea shells (Meinhardt–Gierer PDE). The results achieved enforce the role of SC-CNNs as universal paradigm for the generation of nonlinear, complex dynamics.

[1]  P. Arena,et al.  Chua's circuit can be generated by CNN cells , 1995 .

[2]  Barrie Gilbert.  A high-performance monolithic multiplier using active feedback , 1974 .

[3]  P. Arena,et al.  Self-organization in a two-layer CNN , 1998 .

[4]  J. Sutherland.  The Quark and the Jaguar , 1994 .

[5]  Christian Heite,et al.  Analog CMOS realization of fuzzy logic membership functions , 1993 .

[6]  E. Seevinck,et al.  CMOS translinear circuits for minimum supply voltage , 2000 .

[7]  Chauncey D. Leake,et al.  British Association for the Advancement of Science , 1953, Science.

[8]  Rabinder N Madan,et al.  Chua's Circuit: A Paradigm for Chaos , 1993, Chua's Circuit.

[9]  L. Chua.  Passivity and complexity , 1999 .

[10]  I. Prigogine,et al.  Exploring Complexity: An Introduction , 1989 .

[11]  I. Stewart,et al.  Life's other secret : the new mathematics of the living world , 1998 .

[12]  Á. Rodríguez-Vázquez,et al.  A piecewise-linear function approximation using current mode circuits , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[13]  R. Hirota.  Exact solution of the Korteweg-deVries equation for multiple collision of solitons , 1971 .

[14]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[15]  A. Scott,et al.  The soliton: A new concept in applied science , 1973 .

[16]  Luigi Fortuna,et al.  A generalized Chua Cell for Realizing any continuous n-Segment piecewise-Linear Function , 2001, Int. J. Bifurc. Chaos.

[17]  Alwyn C. Scott,et al.  Nonlinear Science: Emergence and Dynamics of Coherent Structures , 1999 .

[18]  Zheng Tang,et al.  Four-quadrant CMOS current-mode multiplier independent of device parameters , 2000 .

[19]  K. Kimura,et al.  Some circuit design techniques for low-voltage analog functional elements using squaring circuits , 1996 .