## 7 Conclusion 

In this paper, we investigate the existence as well as the exponential stability of almost periodic solutions in a new model of SICNNs. The usage of the functional response on alternate (advanced-delayed) type of piecewise constant arguments is the main novelty of our study, and it is useful for the investigation of a large class of neural networks. An illustrative example is provided to show the effectiveness of the theoretical results. 

Our approach concerning exponential stability may be used in the future to investigate synchroniza- tion of chaos in coupled neural networks and control of chaos in large communities of neural networks with piecewise constant argument. 

Differential equations with functional response on piecewise constant argument can be applied for the development of other kinds of recurrent networks such as Hopfield and Cohen-Grossberg neural networks [81, 82] and others. This will provide new opportunities for the analysis and applications of neural networks. 

## Acknowledgments 

The authors wish to express their sincere gratitude to the referees for the helpful criticism and valuable suggestions, which helped to improve the paper significantly. 

The second author is supported by the 2219 scholarship programme of TÜBİTAK, the Scientific and Technological Research Council of Turkey. 

## References 

[1] Chua LO (1998) CNN: A Paradigm for complexity. World Scientific, Singapore. 

[2] Chua LO, Yang L (1988) Cellular neural networks: theory. IEEE Trans Circuits Syst 35:1257–1272. 

[3] Chua LO, Yang L (1988) Cellular neural networks: applications. IEEE Trans Circuits Syst 35:1273– 1290. 

[4] Chua LO, Roska T (1990) Cellular neural networks with nonlinear and delay-type template ele- ments. In: Proceedings of IEEE International Workshop on Cellular Neural Networks and Their Applications, pp 12–25. 

[5] Chua LO, Roska T (1992) Cellular neural networks with nonlinear and delay type template elements and non-uniform grids. Int J Circuit Theory Appl 20:449–451. 

[6] Hsu C-H, Lin S-S, Shen W (1999) Traveling waves in cellular neural networks. International Journal of Bifurcation and Chaos 9:1307–1319. 

