Dr. Akylbek Zhamanshin,
Herriot-Watt University Aktobe Campus, Kazakhstan
UNPREDICTABILITY IN COHEN-GROSSBERG NEURAL NETWORKS
Cohen–Grossberg neural networks were firstly proposed by Cohen M. and Grossberg S. in 1983 [1]. The class of models has intensive applications within various engineering and scientific fields such as neuro-biology, population dynamics and computing technology. Moreover, Cohen–Grossberg neural networks include as sub-classes cellular and Hopfield neural networks. This is why, many researchers are focused on investigating the dynamics of Cohen–Grossberg neural networks, in particular, periodic and almost periodic oscillations. In turn, a few years ago, Professor Akhmet M. and his colleague extended the concept of recurrent motions to unpredictable ones [2]. The newly introduced movements have chaotic dynamics. In our study, we provide theoretical as well as numerical results for recurrent oscillations in Cohen-Grossberg neural networks with variable inputs and strengths of connectivity for cells, which are unpredictable functions. A special case, when the coefficients are compartmental with periodic and unpredictable ingredients is also carefully researched. By numerical and graphical analysis, it is shown how a constructive technical characteristic, the degree of periodicity, reflects contributions of the ingredients in final outputs of the neural networks. Sufficient conditions are obtained to guarantee the existence of exponentially stable unpredictable outputs of the models. They are specified for Poisson stability by utilizing the original method of included intervals. Examples with numerical simulations that support the theoretical results are provided.
References
1. M. Cohen, S. Grossberg, Absolute stability and global pattern formation and parallel memory storage by competitive neural networks, IEEE Trans Syst Man Cybernet 13 (1983) 815–826.
2. M. Akhmet, M. Fen, Poincare chaos and unpredictable functions, Communications in Nonlinear Science and Numerical Simulation 48 (2017), 85–94.
