Akif Akgul

Hidden hyperchaos and electronic circuit application in a 5D self-exciting homopolar disc dynamo

We report on the finding of hidden hyperchaos in a 5D extension to a known 3D self-exciting homopolar disc dynamo. The hidden hyperchaos is identified through three positive Lyapunov exponents under the condition that the proposed model has just two stable equilibrium states in certain regions of parameter space. The new 5D hyperchaotic self-exciting homopolar disc dynamo has multiple attractors including point attractors, limit cycles, quasi-periodic dynamics, hidden chaos or hyperchaos, as well as coexisting attractors. We use numerical integrations to create the phase plane trajectories, produce bifurcation diagram, and compute Lyapunov exponents to verify the hidden attractors. Because no unstable equilibria exist in two parameter regions, the system has a multistability and six kinds of complex dynamic behaviors. To the best of our knowledge, this feature has not been previously reported in any other high-dimensional system. Moreover, the 5D hyperchaotic system has been simulated using a specially designed electronic circuit and viewed on an oscilloscope, thereby confirming the results of the numerical integrations. Both Matlab and the oscilloscope outputs produce similar phase portraits. Such implementations in real time represent a new type of hidden attractor with important consequences for engineering applications.

A new three-dimensional chaotic system without equilibrium points, its dynamical analyses and electronic circuit application

Original scientific paper In this paper, a new three-dimensional chaotic system without equilibrium points is introduced and analysed. Basic dynamical analysis of this new chaotic system without equilibrium points is carried out by means of system equilibria, phase portraits, sensitivity to initial conditions, fractal dimension and chaotic behaviours. In addition, in this paper Lyapunov exponents spectrum and bifurcation analysis of the proposed chaotic system have been executed by means of selected parameters. The chaotic system without equilibrium points has been executed by detailed theoretical analysis as well as simulations with designed electronical circuit. A chaotic system without equilibrium points is also known as chaotic system with hidden attractor and there are very few researches in the literature. Since they cannot have homoclinic and heteroclinic orbits, Shilnikov method cannot be applied to find whether the system is chaotic or not. Therefore, it can be useful in many engineering applications, especially in chaos based cryptology and coding information. Furthermore, introduced chaotic system without equilibrium points in this paper can have many unknown dynamical behaviours. These behaviours of the strange chaotic attractors deserve further investigation.

A new chaotic oscillator with free control

A novel chaotic system is explored in which all terms are quadratic except for a linear function. The slope of the linear function rescales the amplitude and frequency of the variables linearly while its zero intercept allows offset boosting for one of the variables. Therefore, a free-controlled chaotic oscillation can be obtained with any desired amplitude, frequency, and offset by an easy modification of the linear function. When implemented as an electronic circuit, the corresponding chaotic signal can be controlled by two independent potentiometers, which is convenient for constructing a chaos-based application system. To the best of our knowledge, this class of chaotic oscillators has never been reported.

Various Types of Coexisting Attractors in a New 4D Autonomous Chaotic System

An unique 4D autonomous chaotic system with signum function term is proposed in this paper. The system has four unstable equilibria and various types of coexisting attractors appear. Four-wing and ...

A New Chaotic Flow with Hidden Attractor: The First Hyperjerk System with No Equilibrium

Abstract Discovering unknown aspects of non-equilibrium systems with hidden strange attractors is an attractive research topic. A novel quadratic hyperjerk system is introduced in this paper. It is noteworthy that this non-equilibrium system can generate hidden chaotic attractors. The essential properties of such systems are investigated by means of equilibrium points, phase portrait, bifurcation diagram, and Lyapunov exponents. In addition, a fractional-order differential equation of this new system is presented. Moreover, an electronic circuit is also designed and implemented to verify the feasibility of the theoretical model.

A New Chaotic System with a Self-Excited Attractor: Entropy Measurement, Signal Encryption, and Parameter Estimation

In this paper, we introduce a new chaotic system that is used for an engineering application of the signal encryption. It has some interesting features, and its successful implementation and manufacturing were performed via a real circuit as a random number generator. In addition, we provide a parameter estimation method to extract chaotic model parameters from the real data of the chaotic circuit. The parameter estimation method is based on the attractor distribution modeling in the state space, which is compatible with the chaotic system characteristics. Here, a Gaussian mixture model (GMM) is used as a main part of cost function computations in the parameter estimation method. To optimize the cost function, we also apply two recent efficient optimization methods: WOA (Whale Optimization Algorithm), and MVO (Multi-Verse Optimizer) algorithms. The results show the success of the parameter estimation procedure.

Amplitude Control Analysis of a Four-Wing Chaotic Attractor, its Electronic Circuit Designs and Microcontroller-Based Random Number Generator

An exhaustive analysis of a four-wing chaotic system is presented in this paper. It is proved that the evolution range of some variables can be modulated easily by one coefficient of a cross product term. An amplitude-adjustable chaotic circuit is designed, which shows a good agreement with the theoretical analysis. Also, in this paper a microcontroller-based random number generator (RNG) was designed with a nonlinear four-wing chaotic system. RNG studies of the current time have been usually carried out with complicated structures that are costly and difficult to use in real time implementations and that require so much energy consumption. On the other hand, in this paper, as opposed to the disadvantages mentioned here, a microcontroller-based RNG was designed with a four-wing chaotic system (also discussed in the paper) and this was introduced to literature. Microcontroller-based random numbers that passed randomness tests will be available for use in many fields in real life, particularly in encryption.

A Switchable Chaotic Oscillator with Two Amplitude–Frequency Controllers

A simple chaotic system with a single nonquadratic term is developed to be a switchable chaotic signal generator in this paper. Additional nonlinearity of the absolute value function is introduced for reforming the structure without damaging the basic dynamics but yielding a new independent amplitude–frequency controller. A switchable chaotic experimental oscillator is designed afterwards, where two coefficients corresponding to two independent rheostats rescale the amplitude and frequency of the chaotic signals smoothly. To our knowledge, this has never been found in other chaotic oscillators.

Synchronization and Electronic Circuit Application of Hidden Hyperchaos in a Four-Dimensional Self-Exciting Homopolar Disc Dynamo without Equilibria

We introduce and investigate a four-dimensional hidden hyperchaotic system without equilibria, which is obtained by augmenting the three-dimensional self-exciting homopolar disc dynamo due to Moffatt with an additional control variable. Synchronization of two such coupled disc dynamo models is investigated by active control and sliding mode control methods. Numerical integrations show that sliding mode control provides a better synchronization in time but causes chattering. The solution is obtained by switching to active control when the synchronization errors become very small. In addition, the electronic circuit of the four-dimensional hyperchaotic system has been realized in ORCAD-PSpice and on the oscilloscope by amplitude values, verifying the results from the numerical experiments.

Text encryption by using one-dimensional chaos generators and nonlinear equations

In this study, a chaos based encryption method with nonlinear equations in MATLAB environment is proposed to increase communication security. Encryption methods that generated by using the properties of three different chaos generators are analyzed. Logistic Map, Pinchers Map and Sine-Circle Map chaos generators which are commonly referred in the literature are used to realize applications. Performance is analyzed by using time and entropy values.