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

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

The Concept of Unidirectionally Coupled Nonlinear Circuits via a Memristor

Confirmation of the existence of memristor by researchers at 2008 attracts much interest on this newly found circuit element. This is due to the fact that memristor opens up new functionalities in electronics and it has led to the interpretation of phenomena regarding not only electronics but also biological systems. In this work, we have studied the simulated dynamic behavior of two unidirectionally coupled nonlinear circuits via a memristor. This confirms the transition from chaotic desynchronization to complete chaotic synchronization through a regime of intermittent synchronization between the unidirectionally coupled circuits

Analysis, Adaptive Control and Synchronization of a Seven-Term Novel 3-D Chaotic System with Three Quadratic Nonlinearities and its Digital Implementation in LabVIEW

This research work proposes a seven-term novel 3-D chaotic system with three quadratic nonlinearities and analyses the fundamental properties of the system such as dissipativity, symmetry, equilibria, Lyapunov exponents and Kaplan-Yorke dimension. The phase portraits of the novel chaotic system simulated using MATLAB depict the strange chaotic attractor of the novel system. For the parameter values and initial conditions chosen in this work, the Lyapunov exponents of the novel chaotic system are obtained as �! = 2.71916, �! = 0 and �! = −13.72776. Also, the KaplanYorke dimension of the novel chaotic system is obtained as �!" = 2.19808. Next, an adaptive controller is designed to stabilize the novel chaotic system with unknown system parameters. Also, an adaptive controller is designed to achieve global chaos synchronization of two identical novel chaotic systems with unknown system parameters. Finally, an electronic circuit realization of the novel chaotic system is depicted using LabVIEW to confirm the feasibility of the theoretical chaotic model