Enhancing Chaos Complexity of a Plasma Model through Power Input with Desirable Random Features

Dynamics of chaotic system based on circuit design with Ulam stability through fractal-fractional derivative with power law kernel

In this paper, the newly developed Fractal-Fractional derivative with power law kernel is used to analyse the dynamics of chaotic system based on a circuit design. The problem is modelled in terms of classical order nonlinear, coupled ordinary differential equations which is then generalized through Fractal-Fractional derivative with power law kernel. Furthermore, several theoretical analyses such as model equilibria, existence, uniqueness, and Ulam stability of the system have been calculated. The highly non-linear fractal-fractional order system is then analyzed through a numerical technique using the MATLAB software. The graphical solutions are portrayed in two dimensional graphs and three dimensional phase portraits and explained in detail in the discussion section while some concluding remarks have been drawn from the current study. It is worth noting that fractal-fractional differential operators can fastly converge the dynamics of chaotic system to its static equilibrium by adjusting the fractal and fractional parameters.

An Oscillator without Linear Terms: Infinite Equilibria, Chaos, Realization, and Application

Oscillations and oscillators appear in various fields and find applications in numerous areas. We present an oscillator with infinite equilibria in this work. The oscillator includes only nonlinear elements (quadratic, absolute, and cubic ones). It is different from common oscillators, in which there are linear elements. Special features of the oscillator are suitable for secure applications. The oscillator’s dynamics have been discovered via simulations and an electronic circuit. Chaotic attractors, bifurcation diagrams, Lyapunov exponents, and the boosting feature are presented while measurements of the implemented oscillator are reported by using an oscilloscope. We introduce a random number generator using such an oscillator, which is applied in biomedical image encryption. Moreover, the security and performance analysis are considered to confirm the correctness of encryption and decryption processes.

Chaotic Dynamics by Some Quadratic Jerk Systems

This paper is about the dynamical evolution of a family of chaotic jerk systems, which have different attractors for varying values of parameter a. By using Hopf bifurcation analysis, bifurcation diagrams, Lyapunov exponents, and cross sections, both self-excited and hidden attractors are explored. The self-exited chaotic attractors are found via a supercritical Hopf bifurcation and period-doubling cascades to chaos. The hidden chaotic attractors (related to a subcritical Hopf bifurcation, and with a unique stable equilibrium) are also found via period-doubling cascades to chaos. A circuit implementation is presented for the hidden chaotic attractor. The methods used in this paper will help understand and predict the chaotic dynamics of quadratic jerk systems.

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.

SIEA: Secure Image Encryption Algorithm Based on Chaotic Systems Optimization Algorithms and PUFs

One of the general problems in modern digital society is undoubtedly the information security topic. It is critical to ensure the security of information transferred, processed, and stored throughout digital channels. Among this information, digital images draw attention in terms of frequency of use in digital channels. In this study, a new image encryption algorithm is proposed to address the security problems of digital images. The aspect that differentiates the proposed algorithm from thousands of image encryption algorithms in the literature is that it is designed within the framework of the provable security design principle. The provable security design approach has ensured that the proposed algorithm is theoretically secure with mathematical proof techniques. In addition to addressing the proposed architecture security concerns, the hybrid random number generator used as the key generator constitutes another unique aspect. This generator, which was designed using chaotic systems, physical unclonable functions, and optimization algorithms, stands out as the innovative aspect of the study. The statistical randomness properties of the proposed random number generator were tested using the NIST SP 800-22 Statistical Test Suite. Successful results were obtained for 15 tests in the test package. In addition, the success of these outputs was tested on a new image encryption algorithm. The security of the proposed algorithm was tested from different angles using various experimental analyzes and a 12-step provable security analysis roadmap. Successful analysis results and performance measurements indicate that the proposed cryptographic components can be used in many information security applications and many future designs.

Complexity and Chimera States in a Network of Fractional-Order Laser Systems

By applying the Adams-Bashforth-Moulton method (ABM), this paper explores the complexity and synchronization of a fractional-order laser dynamical model. The dynamics under the variance of derivative order q and parameters of the system have examined using the multiscale complexity algorithm and the bifurcation diagram. Numerical simulation outcomes demonstrate that the system generates chaos with the decreasing of q. Moreover, this paper designs the coupled fractional-order network of laser systems and subsequently obtains its numerical solution using ABM. These solutions have demonstrated chimera states of the proposed fractional-order laser network.