ABSTRACT
Fractional-order (FO) chaotic systems exhibit random sequences of significantly greater complexity when compared to integer-order systems. This feature makes FO chaotic systems more secure against various attacks in image cryptosystems. In this study, the dynamical characteristics of the FO Sprott K chaotic system are thoroughly investigated by phase planes, bifurcation diagrams, and Lyapunov exponential spectrums to be utilized in biometric iris image encryption. It is proven with the numerical studies the Sprott K system demonstrates chaotic behaviour when the order of the system is selected as 0.9. Afterward, the introduced FO Sprott K chaotic system-based biometric iris image encryption design is carried out in the study. According to the results of the statistical and attack analyses of the encryption design, the secure transmission of biometric iris images is successful using the proposed encryption design. Thus, the FO Sprott K chaotic system can be employed effectively in chaos-based encryption applications.
ABSTRACT
A chaotic map with two-dimensional offset boosting is exhaustively studied, which is derived from the Lozi map and shows the controllability of amplitude control. The mechanism of two-dimensional offset boosting is revealed based on the cancelation of offset-involved feedback terms. Furthermore, the coexistence of homogeneous multistability and heterogeneous multistability is disclosed when the offset boosting turns to the initial condition. It is also found that the independent constant term rescales the amplitude of all the sequences without changing the Lyapunov exponents. More strikingly, the parameters for amplitude control and offset boosting are bound together introducing hybrid control. The circuit implementation based on the microcontroller unit is used to validate the theoretical analysis and numerical simulations. This chaotic map is applied for particle swarm optimization showing its stronger performance and robustness in solving optimization problems.
ABSTRACT
Complex biorhythms are characteristic of ubiquitous phenomena appearing in many disciplines of human knowledge. This Special Issue collects articles devoted to different complex biorhythms phenomena such as cardiac dynamics, Covid-19 dynamics, dynamics of neural networks, cell dynamics, and a few articles devoted to general methods. It furnishes a rich overview of the field and can stimulate and inspire further researches.
ABSTRACT
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.
ABSTRACT
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.
ABSTRACT
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.
ABSTRACT
This paper reports about a novel three-dimensional chaotic system with three nonlinearities. The system has one stable equilibrium, two stable equilibria and one saddle node, two saddle foci and one saddle node for different parameters. One salient feature of this novel system is its multiple attractors caused by different initial values. With the change of parameters, the system experiences mono-stability, bi-stability, mono-periodicity, bi-periodicity, one strange attractor, and two coexisting strange attractors. The complex dynamic behaviors of the system are revealed by analyzing the corresponding equilibria and using the numerical simulation method. In addition, an electronic circuit is given for implementing the chaotic attractors of the system. Using the new chaotic system, an S-Box is developed for cryptographic operations. Moreover, we test the performance of this produced S-Box and compare it to the existing S-Box studies.
