20 research outputs found
An Eight-Term Novel Four-Scroll Chaotic System with Cubic Nonlinearity and its Circuit Simulation
This research work proposes an eight-term novel four-scroll chaotic system with cubic nonlinearity and analyses its
fundamental properties such as dissipativity, equilibria, symmetry and invariance, Lyapunov exponents and KaplanYorke
dimension. The phase portraits of the novel chaotic system, which are obtained in this work by using MATLAB,
depict the four-scroll attractor of the system. For the parameter values and initial conditions chosen in this work, the
Lyapunov exponents of the novel four-scroll chaotic system are obtained as L1 = 0.75335, L2 = 0 and L3 = −22.43304.
Also, the Kaplan-Yorke dimension of the novel four-scroll chaotic system is obtained as DKY = 2.0336. Finally, an
electronic circuit realization of the novel four-scroll chaotic system is presented by using SPICE to confirm the
feasibility of the theoretical model
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
Analysis, Control, Synchronization and SPICE Implementation of a Novel 4-D Hyperchaotic Rikitake Dynamo System without Equilibrium
Chaos theory has wide applications and its importance can be seen by the voluminous publications on various
applications in several branches of science, commerce and engineering. Control, tracking or regulation and
synchronization of different types of chaotic systems are importance areas of research in the control literature and
various methods have been adopted over the past few decades for tackling these research problems. Also, the discovery
of novel chaotic and hyperchaotic systems in various applications, their qualitative properties and the control of such
systems are also important research areas in chaos theory. This paper announces a novel 4-D hyperchaotic Rikitake
dynamo system, which is derived by adding a state feedback control to the famous 3-D Rikitake two-disk dynamo
system (1958). The frequent and irregular reversals of the Earth’s magnetic field inspired a number of early studies
involving electrical currents within the Earth’s molten core. One of the first such models to exhibit reversals was
Rikitake’s two-disk dynamo system (Rikitake, 1958). This paper discusses the qualitative properties of the novel
hyperchaotic Rikitake dynamo system. We note that the novel hyperchaotic Rikitake dynamo system has no equilibrium
points. The Lyapunov exponents of the hyperchaotic Rikitake dynamo system are found as �! = 0.09136, �! =
0.02198, �! = 0 and �! = −2.11190. The Kaplan-Yorke fractional dimension of the novel hyperchaotic Rikitake
dynamo system is found as �!" = 3.05367. Next, this paper discusses control and synchronization of the novel
hyperchaotic Rikitake dynamo system with unknown parameters using adaptive control method. The main results are
established using Lyapunov stability theory and numerically illustrated using MATLAB. Finally, for the 4-D novel
hyperchaotic system, an electronic circuit realization in SPICE has been described to confirm the feasibility of the
theoretical hyperchaotic Rikitake dynamo model
Analysis, Adaptive Control and Adaptive Synchronization of a Nine-Term Novel 3-D Chaotic System with Four Quadratic Nonlinearities and its Circuit Simulation
This research work describes a nine-term novel 3-D chaotic system with four quadratic nonlinearities and details its
qualitative properties. The phase portraits of the 3-D novel chaotic system simulated using MATLAB, depict the strange
chaotic attractor of the system. For the parameter values chosen in this work, the Lyapunov exponents of the novel
chaotic system are obtained as L1 = 6.8548, L2 = 0 and L3 = −32.8779. Also, the Kaplan-Yorke dimension of the novel
chaotic system is obtained as DKY = 2.2085. Next, an adaptive controller is design to achieve global stabilization of the
3-D novel chaotic system with unknown system parameters. Moreover, 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 presented using SPICE to confirm the feasibility of the
theoretical model
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
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
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
The Study of a Nonlinear Duffing – Type Oscillator Driven by Two Voltage Sources
In the present work, a detailed study of a nonlinear electrical oscillator with damping and external excitation is
presented. The system under study consists of a Duffing-type circuit driven by two sinusoidal voltage sources having
different frequencies. The dynamical behavior of the proposed system is investigated numerically, by solving the system
of state equations and simulating its behavior as a circuit using MultiSim. The tools of the theoretical approach are the
bifurcation diagrams, the Poincaré sections, the phase portraits, and the maximum Lyapunov exponent. The numerical
investigation showed that the system has rich complex dynamics including phenomena such as quasiperiodicity, 3-tori,
and chaos