ABSTRACT
This chapter is a continuation of the work given in (Zeraoulia & Sprott (2011(g))) where the details of this particular topic are not discussed enough. In this chapter, we discuss robust chaos in neural networks with many illustrating examples and methods. Indeed, in Sec. 4.2, we give an overview of chaos in the field of neural networks with some suggested applications. Sec. 4.3 deals with the method of weight-space exploration that can used to predict robust chaos in neural networks. In Sec. 4.3.1, we give an example of robust chaos generated by a neural networks with a smooth activation function. While in Sec. 4.3.2, we give an example of fragile chaos generated by a neural networks with a smooth activation function. In Sec. 4.3.3 we present and discuss robust chaos in the case of blocks with non-smooth activation function. In Sec. 4.3.4 we present and discuss robust chaos in the electroencephalogram model by using numerical calculations. As a very important result, we present in Sec. 4.3.5 an example of robust chaos in diluted circulant networks by using the largest Lyapunov exponent as a signature for chaos. In Sec. 4.3.6, we discuss robust chaos in non-smooth neural networks. Finally, in Sec. 4.4 a collection of open problems is given concerning some aspects relating mathematics to the notion of robust chaos.
