We present the design of an autonomous time-delay Boolean network realized with readily available electronic components. Through simulations and experiments that account for the detailed nonlinear response of each circuit element, we demonstrate that a network with five Boolean nodes displays complex behavior. Furthermore, we show that the dynamics of two identical networks display near-instantaneous synchronization to a periodic state when forced by a common periodic Boolean signal. A theoretical analysis of the network reveals the conditions under which complex behavior is expected in an individual network and the occurrence of synchronization in the forced networks. This research will enable future experiments on autonomous time-delay networks using readily available electronic components with dynamics on a slow enough time-scale so that inexpensive data collection systems can faithfully record the dynamics.

No abstract

Parameters of the electronic components. We set the parameters of Eqs. (2)-(4) in order to have chaotic dynamics at the Rössler oscillators. The main advantage of being in such a regime is that the order parameter r is a good indicator of the global synchronization of the network, which allows relating the reported values of the identifiability parameter with the level of synchronization of the whole network. The specific values of the electronic components are summarized in Table 1. Circuit diagrams. The Rössler oscilator. We use the Rössler system described in Ref. 30 , which is composed of a combination of resistances, capacitors, diodes and operational amplifiers (Op-Amp). All parameters are fixed and equal to all oscillators. Figure 7 contains the circuit diagram.

The obtainment of a dynamical logic gate (DLG), which is a device capable of implementing several logic functions using the same model, has been one of the goals of the scientific community. Dynamical systems, specifically those that display chaotic behavior, have been widely used to emulate different logic gates which are the basis of general-purpose computing. In this study, we present a methodology based on unstable dissipative systems of type 1 (UDS-1), a kind of dynamical system capable of generating multi-scrolls and multi-stability. Using these two features, we codify inputs, subsequently, we get the adequate output, developing in this way a dynamical (reconfigurable) logic gate that performs any of the sixteen possible logic functions of two inputs. A highlight of the proposed methodology is that the selection of the desired logic gate is realized just by varying a couple of parameters.

Considerado como el cuarto elemento pasivo en la teoría de circuitos, un memristor puede ser utilizado para diseñar sistemas caóticos e incrementar su complejidad. En este artículo se presenta la generación de atractores autoexcitados, coexistentes y ocultos. Las diferentes familias de atractores se generan al agregar la función no lineal de un memristor controlado por flujo a un sistema caótico. La riqueza de la dinámica caótica en el sistema es investigada a través de diagramas de bifurcación, exponentes de Lyapunov, planos de fase y dimensión KaplanYorke. Estos métodos muestran que en un rango de parámetros, el sistema caótico propuesto presenta atractores caóticos coexistentes. Finalmente, el sistema caótico es diseñado con circuitos electrónicos analógicos. Los resultados obtenidos de la simulación del circuito electrónico están en concordancia con los resultados de los análisis teóricos y numéricos.