Bifurcation Analysis of Reduced Network Model of Coupled Gaussian Maps for Associative Memory

Mio  Kobayashi; Tetsuya  Yoshinaga

doi:10.4236/ijmnta.2019.81001

Mio Kobayashi¹, Tetsuya Yoshinaga²

Abstract: This paper proposes an associative memory model based on a coupled system of Gaussian maps. A one-dimensional Gaussian map describes a discrete-time dynamical system, and the coupled system of Gaussian maps can generate various phenomena including asymmetric fixed and periodic points. The Gaussian associative memory can effectively recall one of the stored patterns, which were triggered by an input pattern by associating the asymmetric two-periodic points observed in the coupled system with the binary values of output patterns. To investigate the Gaussian associative memory model, we formed its reduced model and analyzed the bifurcation structure. Pseudo-patterns were observed for the proposed model along with other conventional associative memory models, and the obtained patterns were related to the high-order or quasi-periodic points and the chaotic trajectories. In this paper, the structure of the Gaussian associative memory and its reduced models are introduced as well as the results of the bifurcation analysis are presented. Furthermore, the output sequences obtained from simulation of the recalling process are presented. We discuss the mechanism and the characteristics of the Gaussian associative memory based on the results of the analysis and the simulations conducted.

Keywords: Gaussian Map, Associative Memory Model, Bifurcation Analysis, Discrete-Time Dynamical System

Cite this paper: Kobayashi, M. and Yoshinaga, T. (2019) Bifurcation Analysis of Reduced Network Model of Coupled Gaussian Maps for Associative Memory. International Journal of Modern Nonlinear Theory and Application, 8, 1-16. doi: 10.4236/ijmnta.2019.81001.

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