Double Scroll Circuit Research Articles

Application of particle swarm optimization with ANFIS model for double scroll chaotic system

The predictions for the original chaos patterns can be used to correct the distorted chaos pattern which has changed due to any changes whether from undesired disturbance or additional information which can hide under chaos pattern. This information can be recovered when the original chaos pattern is predicted. But unpredictability is most features of chaos, and time series prediction can be used based on the collection of past observations of a variable and analysis it to obtain the underlying relationships and then extrapolate future time series. The additional information often prunes away by several techniques. This paper shows how the chaotic time series prediction is difficult and distort even if Neuro-Fuzzy such as Adaptive Neural Fuzzy Inference System (ANFIS) is used under any disturbance. The paper combined particle swarm (PSO) and (ANFIS) to exam the prediction model and predict the original chaos patterns which comes from the double scroll circuit. Changes in the bias of the nonlinear resistor were used as a disturbance. The predicted chaotic data is compared with data from the chaotic circuit.

Experimental investigation of amplitude death in delay-coupled double-scroll circuits with randomly time-varying network topology

The present study experimentally investigates amplitude death in delay-coupled double-scroll circuits with a time-varying network topology that randomly changes at a regular interval. Circuit experiments show that amplitude death can occur in the time-varying network. Furthermore, the experimental results well agree with the analytical results obtained based on a time-averaged adjacency matrix when the interval is much shorter than the natural period of the double-scroll circuits.

Chaos synchronization of a chain network based on a sliding mode control

A sliding mode control approach is proposed to implement the synchronization of the chain tree network. The double-scroll circuit chaos systems are treated as nodes and the network is constructed with the state variable coupling. By selecting a switching sliding surface, the chaos synchronization of the network is achieved with one control input only. The stability analysis and the numerical simulations demonstrate that the complete synchronization in a chain network can be realized for all nodes.

IMPLEMENTATION OF A CHUA CIRCUIT TO DEMONSTRATE BIFURCATIONS AND STRANGE ATTRACTORS IN A CLASS

This paper describes the design and implementation of a Chua double-scroll circuit to demonstrate chaos in dynamical systems to students in a graduate course in order to enhance their visualization and understanding of strange attractor and Feigenbaum bifurcation trees.Teaching dynamical systems (i.e., nonlinear systems that can exhibit chaos) is often considered difficult because of the mathematical modeling involved and the inclusion of the fourth strange-attractor state, in addition to the traditional point stability, cyclic stability, and toroidal stability, as found in dynamic systems. A graduate course has been offered at the University of Manitoba for many years to provide both (i) a unified theory of fractal dimensions, together with many practical implementations of algorithms to compute the fractal dimensions, including the Rényi dimension spectrum that is required for characterization of the strange attractors using multifractal analysis.Leon Chua developed a simple nonlinear circuit capable of producing a rich collection of dynamic phenomena, ranging from fixed points to cycle points, standard bifurcations (period doubling), other standard routes to chaos, and chaos itself. The reason for selecting this specific circuit as a class demonstration tool is threefold: (i) the circuit has an analytical model and can be simulated, (ii) the circuit is implementable using available commercial off-the-shelf components, and (iii) the signals in the circuit can be acquired without affecting and altering its operation significantly.This paper describes the architecture, implementation, verification, and testing of the Chua system, as well as an analysis of the data obtained during the current phase of the development. Although there are many possible implementations of Chua’s circuit, our implementation has several innovative design features to make it more applicable to enhance students’ learning in the classroom.

Non-smooth bifurcations in a double-scroll circuit with periodic excitation

The fast-slow effect can be observed in a typical non-smooth electric circuit with order gap between the natural frequency and the excitation frequency. Numerical simulations are employed to show complicated behaviours, especially different types of busting phenomena. The bifurcation mechanism for the bursting solutions is analysed by assuming the forms of the solutions and introducing the generalized Jacobian matrix at the non-smooth boundaries, which can also be used to account for the evolution of the complicated structures of the phase portraits with the variation of the parameter. Period-adding bifurcation has been explored through the computation of the eigenvalues related to the solutions. At the non-smooth boundaries the so-called ‘single crossing bifurcation’ can occur, corresponding to the case where the eigenvalues jump only once across the imaginary axis, which leads the periodic burster to have a quasi-periodic oscillation.

Various synchronization phenomena in bidirectionally coupled double scroll circuits

In this paper, the various cases of synchronization phenomena investigated in a system of two bidirectionally coupled double scroll circuits, were studied. Complete synchronization, inverse lag synchronization, and inverse π-lag synchronization are the observed synchronization phenomena, as the coupling factor is varied. The inverse lag synchronization phenomenon in mutually coupled identical oscillators is presented for the first time. As the coupling factor is increased, the system undergoes a transition from chaotic desynchronization to chaotic complete synchronization, while inverse lag synchronization and inverse π-lag synchronization are observed for greater values of the coupling factor, depending on the initial conditions of the state variables of the system. Inverse π-lag synchronization in coupled nonlinear oscillators is a special case of lag synchronization, which is also presented for the first time.

Delayed feedback control based on the act-and-wait concept

This paper proposes a delayed feedback control (DFC) based on the act-and-wait concept, which reduces the dynamics of DFC systems to that of discrete-time systems. Based on this concept, a delayed feedback controller is designed for a prototype two-dimensional oscillator using a simple systematic procedure. This control has two advantages: the feedback delay time can be large and it can obtain deadbeat behavior. A numerical example using a double-scroll circuit model demonstrates these theoretical results.

Master–Slave double–scroll circuit incomplete synchronization

The experimental study of the route from synchronization to desynchronization of a master-slave configuration of doublescroll circuits, is presented. The parameter controlling the system synchronization was the coupling resistance between the master-slave circuits. In the region between synchronization-desynchronization, it was shown that an intermediate regime of incomplete synchronization emerged. The study of the related dynamics proved that this incomplete synchronization was of the on-off intermittency kind.

Stabilization of a steady state in network oscillators by using diffusive connections with two long time delays

The present study shows that diffusive connections with two long-time delays can induce the stabilization of a steady state in network oscillators. A linear stability analysis shows that, if the two delay times retain a proportional relation with a certain bias, the stabilization can be achieved independent of the delay times. Furthermore, a simple systematic procedure for designing the coupling strength and the delay times in the connections is proposed. The procedure has the following two advantages: one can employ time delays as long as one wants and the stabilization can be achieved independently of its network topology. Our analytical results are applied to the well-known double-scroll circuit model on a small-world network.

On–off intermittent synchronization between two bidirectionally coupled double scroll circuits

In this report the intermittent route from full synchronization to full desynchronization, of two bidirectionally coupled, double-scroll circuits, was experimentally studied. Coupling resistance, between the two circuits, served as the bifurcation parameter, controlling the synchronization. It was shown that the synchronization–desynchronization transition was realized through a regime of incomplete synchronization of the on–off intermittency type.

HYPERCHAOS IN A CHUA'S CIRCUIT WITH TWO NEW ADDED BRANCHES

In this work a fourth-order Chua's circuit, capable of generating hyperchaotic oscillations in a wide range of parameters, is presented. The circuit is obtained by adding two new branches to the original topology of the Chua's double scroll circuit. One of the added branches is a linear inductor-resistor series connection, and the other one is a nonlinear voltage-controlled current source. A theoretical analysis of the circuit equations is presented, along with numerical and experimental results.

Experimental evidence for spatiotemporal stability in one-way open coupled double-scroll circuits

This paper provides an experimental confirmation of the spatiotemporal stability in one-way open coupled double-scroll circuits. The three-type stability states in the circuits are observed experimentally. Furthermore, we show an experimental procedure to check the spatiotemporal stability.

Spatiotemporal stability of one-way open coupled nonlinear systems

The present paper investigates the spatiotemporal stability of homogeneous solutions in one-way open coupled nonlinear systems. We show that the H(infinity) norm concept, which has been used as an important index in the field of robust control theory, allows us to grasp the mechanism of spatial instability in coupled systems. Spatial instability occurs only when the H(infinity) norm of the transfer function of each site is greater than 1. It is shown that numerical simulations for one-way open coupled double scroll circuits are in good agreement with our theoretical results.

Controlling chaos with simple limiters

New experimental results demonstrate that chaos control can be accomplished using controllers that are very simple relative to the system being controlled. Chaotic dynamics in a driven pendulum and a double scroll circuit are controlled using an adjustable, passive limiter-a weight for the pendulum and a diode for the circuit. For both experiments, multiple unstable periodic orbits are selectively controlled using minimal perturbations. These physical examples suggest that chaos control can be practically applied to a much wider array of important problems than initially thought possible.

Type-II intermittency in the driven Double Scroll Circuit

In this work, we show experimental evidences, confirmed by numerical results, from type-II intermittency in the driven Double Scroll Circuit. Numerically, we found a new scaling power law dependence on the critical parameter. This result is a consequence of the new global bifurcation scenario for the T 2 torus breakdown observed in this system: a homoclinic saddle connection is the nonlinear mechanism responsible for the reinjection of the trajectory around a repelling focus. In fact, in this global scenario the total laminar phase is the spiraling laminar period (usually considered) plus the time the trajectory spends in the vicinity of the saddle points.

Dynamics of the two-frequency torus breakdown in the driven double scroll circuit

In this work we numerically identify three scenarios for the two-frequency torus breakdown to chaos, using the driven double scroll circuit, with varying driving parameters. Two of these scenarios follow the Curry-Yorke route to chaos. For one scenario, we identify the transition to chaos through the onset of a heteroclinic tangle and its heteroclinic points. In the other scenario, chaos appears via period-doubling bifurcations. The third scenario is through the type-II intermittency for which a quasiperiodic torus grows in size, breaks by touching external saddle points, and forms a heteroclinic saddle connection. These dynamic scenarios have distinct structure evolutions: for the Curry-Yorke route, chaos appears softly and alternates with phase locking, while, for the type-II intermittency, chaos appears abruptly and is preserved for a large range of the varying driving parameter.

Easy-to-implement method to target nonlinear systems.

In this work we present a method to rapidly direct a chaotic system, to an aimed state or target, through a sequence of control perturbations, with few different amplitudes chosen according to the allowed control-parameter changes. We applied this procedure to the one-dimensional Logistic map, to the two-dimensional Henon map, and to the Double Scroll circuit described by a three-dimensional system of differential equations. Furthermore, for the Logistic map, we show numerically that the resulting trajectory (from the starting point to the target) goes along a stable manifold of the target. Moreover, using the Henon map, we create and stabilize unstable periodic orbits, and also verify the procedure robustness in the presence of noise. We apply our method to the Double Scroll circuit, without using any low-dimensional mapping to represent its dynamics, an improvement with respect to previous targeting methods only applied for experimental systems that are mapping-modeled. (c) 1998 American Institute of Physics.

Phase-Locking and Bifurcations of the Sinusoidally-Driven Double Scroll Circuit

The dynamic alterations of an electronic circuit in a chaotic regime, described by the Double Scroll attractor, subjected to sinusoidal perturbation are numerically investigated. Parameter diagrams of the circuit phase-locking oscillations in terms of the driving amplitude and frequency are computed. These diagrams have highly interleaved and complex structures, part of them Cantor-like fractals. However, a Cantor-like fractal structure is also observed. In addition, the power spectrum analysis is used to find and characterize three ways of phase-locking the Double Scroll circuit, and to determine how this process depends on the driving parameters. Furthermore, the dynamics of bifurcation phenomena, as chaotic attractor entrainment, Arnold's tongues, coexistence of attractors, and hysteresis are identified in the parameter space.

GLOBAL BIFURCATION ANALYSIS OF THE DOUBLE SCROLL CIRCUIT

An in-depth analysis is made of the global 2-parameter bifurcation structures of the double scroll circuit in terms of their homoclinic, heteroclinic, and periodic orbits. Many fine details are uncovered via a 3-dimensional "unfolding" of the 2-parameter bifurcation structures. Major findings are: (i) The parameter sets which give rise to the homoclinic and heteroclinic orbits (homoclinic and heteroclinic bifurcation sets) studied in this paper are found to be all connected to each other via only one family of periodic orbits. (ii) Moreover, the structure of the windows of this family essentially determines the global structure of the periodic windows of the double scroll circuit. These bifurcation analyses are accomplished by deriving first the relevant bifurcation equations in exact analytic form and then solving these nonlinear equations by iterations. No numerical integration formula for differential equations are used.

Dynamics of the double scroll circuit

Consideration is given to a system of differential equations which has two homoclinic solutions to a same saddle-focus point. The authors prove the existence of a subsystem of solutions which remain in a neighborhood of those homoclinic orbits. In addition to the upper and lower subsystem already described by L. Slinikov's (1965) theorem, this theorem contains solutions that switch in every turn from the neighborhood of one homoclinic to the neighborhood of the other. >