Memristor: A New Concept in Synchronization of Coupled Neuromorphic Circuits

The existence of the memristor, as a fourth fundamental circuit element, by researchers at Hewlett Packard (HP) labs in 2008, has attracted much interest since then. This occurs because the memristor opens up new functionalities in electronics and it has led to the interpretation of phenomena not only in electronic devices but also in biological systems. Furthermore, many research teams work on projects, which use memristors in neuromorphic devices to simulate learning, adaptive and spontaneous behavior while other teams on systems, which attempt to simulate the behavior of biological synapses. In this paper, the latest achievements and applications of this newly development circuit element are presented. Also, the basic features of neuromorphic circuits, in which the memristor can be used as an electrical synapse, are studied. In this direction, a flux-controlled memristor model is adopted for using as a coupling element between coupled electronic circuits, which simulate the behavior of neuron-cells. For this reason, the circuits which are chosen realize the systems of differential equations that simulate the well-known Hindmarsh-Rose and FitzHugh-Nagumo neuron models. Finally, the simulation results of the use of a memristor as an electric synapse present the effectiveness of the proposed method and many interesting dynamic phenomena concerning the behavior of coupled neuron-cells

Complex Dynamics of FitzHugh-Nagumo Type Neurons Coupled with Gap Junction under External Voltage Stimulation

In the present paper, we have studied the complex dynamics of a system of two nonlinear neuronal cells, coupled by a gap junction, which is modelled as a linear variable resistor. The two coupled cells are oscillators of the FitzHughNagumo type. The first cell, the “ImK-cell” is a voltage driven cell, while the second, the “RaLa-cell” is a current driven cell. We have examined the dynamics of the coupled system in the case of bidirectional coupling. An independent voltage source gives the external stimulation. We have examined three different cases (AC, DC, AC plus DC) of the external signal. In each case we have different dynamics. Action potentials, chaotic and periodic oscillations are observed

The Effect of Foreign Direct Investment in Economic Growth from the Perspective of Nonlinear Dynamics

In today’s globalized economy one of the most crucial factors for the economic growth of a country, especially of a developing country, is the foreign direct investment, not only because of the transfer of capital but also of technology. In this work, the effect of foreign direct investments in a county’s economic growth by using tools of nonlinear dynamics is studied. As a model of the economic growth of a country, a well-known nonlinear discrete-time dynamical system, the Logistic map, is used. The system under study consists of two countries with a strong economic relationship. The source country of foreign direct investments is an industrialized, economically powerful and technologically advanced country that makes significant investments in the host country, which is a developing country and strong dependent from the source country. Simulation results of system’s behavior and especially the bifurcation diagrams reveal the strong connection between the countries of the proposed system and the effect of foreign direct investments in the economic growth of the host country

Text Encryption Scheme Realized with a Chaotic Pseudo-Random Bit Generator

In this work a new encryption scheme, which is realized with a Chaotic Pseudo-Random Bit Generator (CPRBG) based on a Logistic map, is presented. The proposed system is used for encrypting text files for the purpose of creating secure data bases. The Logistic map is the most studied discrete nonlinear map because it has been used in many scientific fields. Also, the fact, that this discrete map has a known algebraic distribution, made the Logistic map a good candidate for use in the design of random bit generators. The proposed CPRBG, which is very easily implemented, uses the X-OR function, in the bit sequences, that are produced by two Logistic maps with different initial conditions and system’s parameters, to achieve better results concerning the “randomness” of the produced bits sequence. The detailed results of the statistical testing on generated bit sequences, done by the most well known tests of randomness: the FIPS-140-2 suite tests, confirmed the specific characteristics expected of random bit sequences

A Gallery of Synchronization Phenomena in Resistively Coupled Non-autonomous Chaotic Circuits

This work deals with the study of a variety of synchronization phenomena in the case of resistively coupled nonautonomous, nonlinear circuits. In this paper, a very simple but very representative second order, non-autonomous, nonlinear circuit, is used, the Lacy circuit. Also, two different approaches of coupling between such circuits are applied. The first one is the well-known mutual coupling via a linear resistor, in which the phenomena of complete and anti-phase synchronization are observed and explained based on the nature of this kind of nonlinear systems. The second one is a ring connection in a neural-type system, where the Lacy acts as the master circuit. In this case a very interesting type of partial synchronization, between the other two circuits of this topology, is presented for the first time

Analysis, adaptive control and circuit simulation of a novel finance system with dissaving

In this paper a novel 3-D nonlinear finance chaotic system consisting of two nonlinearities with negative saving term, which is called ‘dissaving’ is presented. The dynamical analysis of the proposed system confirms its complex dynamic behavior, which is studied by using wellknown simulation tools of nonlinear theory, such as the bifurcation diagram, Lyapunov exponents and phase portraits. Also, some interesting phenomena related with nonlinear theory are observed, such as route to chaos through a period doubling sequence and crisis phenomena. In addition, an interesting scheme of adaptive control of finance system’s behavior is presented. Furthermore, the novel nonlinear finance system is emulated by an electronic circuit and its dynamical behavior is studied by using the electronic simulation package Cadence OrCAD in order to confirm the feasibility of the theoretical model