Ricardo Lopez-Ruiz

Ricardo Lopez-Ruiz, Daniele Fournier-Prunaret

In general, the behavior of large and complex aggregates of elementary components can not be understood nor extrapolated from the properties of a few components. The brain is a good example of this type of networked systems where some patterns of behavior are observed independently of the topology and of the number of coupled units. Following this insight, we have studied the dynamics of different aggregates of logistic maps according to a particular {\it symbiotic} coupling scheme that imitates the neuronal excitation coupling. All these aggregates show some common dynamical properties, concretely a bistable behavior that is reported here with a certain detail. Thus, the qualitative relationship with neural systems is suggested through a naive model of many of such networked logistic maps whose behavior mimics the waking-sleeping bistability displayed by brain systems. Due to its relevance, some regions of multistability are determined and sketched for all these logistic models.

Carmen Pellicer-Lostao, Ricardo Lopez-Ruiz

Chaotic cryptography describes the use of chaos theory (in particular physical dynamical systems working in chaotic regime as part of communication techniques and computation algorithms) to perform different cryptographic tasks in a cryptographic system. In the end, the question is, can chaotic systems provide alternative techniques able to enhance cryptographic algorithms?. This chapter can be a worthy material to guide the reader in order to answer himself this question. Thus, the objective of this chapter is to give a general vision of what chaotic cryptography is and a comprehensive example that illustrates the main techniques used in this field.