Dynamic analysis of an improper fractional-order laser chaotic system and its image encryption application

The definition of fractional calculus is introduced into a 3D multi-attribute chaotic system in this paper. The fractional multi-attribute chaotic system (FMACS) numerical solution is obtained based on the Adomian decomposition method (ADM). The balance points and dynamical behaviors of self-excited and hidden attractors in FMACS are compared and analyzed through the Lyapunov spectrum, bifurcation model, and complexity. It is worth noting that some hidden coexistence attractors with different shapes are affected by the order. Besides, a novel chaotic system without equilibrium points is constructed, in which the nonlinear function term in FMACS is replaced with a rare nonlinear function e x . Meanwhile, its degradation phenomenon and state transition phenomenon are analyzed in detail. Finally, the digital circuit of the system is realized on the DSP board. The research result shows that FMACS has richer dynamical behaviors and higher complexity. This research provides a theoretical basis and guidance for the application of fractional chaotic systems.

A fractional-order chaotic system with hidden attractor and self-excited attractor and its DSP implementation

Recently, a lot of research has been done in chaotic cryptography field using different kinds of chaotic systems, like chaotic maps, which are being considered as one of the secure and efficient methods to protect confidential information. This article highlights that the main cryptography requirements demand that the new embedded cryptosystems have to be more efficient and secure, it means that they must be faster and offer greater security. For instance, the new cryptosystems require to be compatible with the new telecommunication protocols and, in addition, to be efficient in energy consumption. In this manner, this article introduces a process to improve the randomness of five chaotic maps that are implemented on a PIC-microcontroller. The improved chaotic maps are tested to encrypt digital images in a wireless communication scheme, particularly on a machine-to-machine (M2M) link, via ZigBee channels. We show that function mod 255 improves the randomness of the pseudo-random number generators (PRNG), which is verified performing NIST SP 800-22 statistical tests, histograms, phase-plane analysis, entropy, correlation of adjacent pixels, differential attacks, and using digital images of size 256 × 256 and 512 × 512 pixels. A comparative analysis is presented versus related works that also use chaotic encryption and classic algorithms, such as: AES, DES, 3DES and IDEA. The security analysis confirms that the proposed process to improve the randomness of chaotic maps, is appropriate to implement an encryption scheme that is secure and robust against several known attacks and other statistical tests. Finally, it was experimentally verified that this chaotic encryption scheme can be used in practical applications such as M2M and Internet of things (IoT).

Randomness improvement of chaotic maps for image encryption in a wireless communication scheme using PIC-microcontroller via Zigbee channels

Abstract : The emerging discipline known as \"chaos theory\" is a relatively new field of study with a diverse range of applications (i.e., economics, biology, meteorology, etc.). Despite this, there is not as yet a universally accepted definition for \"chaos\" as it applies to general dynamical systems. Various approaches range from topological methods of a qualitative description; to physical notions of randomness, information, and entropy in ergodic theory; to the development of computational definitions and algorithms designed to obtain quantitative information. This thesis develops some of the current definitions and discusses several quantitative measures of chaos. It is intended to stimulate the interest of undergraduate and graduate students and is accessible to those with a knowledge of advanced calculus and ordinary differential equations. In covering chaos for continuous systems, it serves as a complement to the work done by Philip Beaver, which details chaotic dynamics for discrete systems.

Introduction of chaotic dynamical systems

Smart cameras and image sensors are widely used in industrial processes, from the designing to the quality checking of the final product. Images generated by these sensors are at continuous risk of disclosure and privacy breach in the industrial Internet of Things (IIoT). Traditional solutions to secure sensitive data fade in IIoT environments because of the involvement of third parties. Blockchain technology is the modern-day solution for trust issues and eliminating or minimizing the role of the third party. In the context of the IIoT, we propose a permissioned private blockchain-based solution to secure the image while encrypting it. In this scheme, the cryptographic pixel values of an image are stored on the blockchain, ensuring the privacy and security of the image data. Based on the number of pixels change rate (NPCR), the unified averaged changed intensity (UACI), and information entropy analysis, we evaluate the strength of proposed image encryption algorithm ciphers with respect to differential attacks. We obtained entropy values near to an ideal value of 8, which is considered to be safe from brute force attack. Encrypted results show that the proposed scheme is highly effective for data leakage prevention and security.

https://www.mdpi.com/1099-4300/22/2/175/pdf

A Blockchain-Based Secure Image Encryption Scheme for the Industrial Internet of Things.

• A novel memristive mega-stable oscillator (MMO) with a plethora of properties is introduced. • The investigation of the volume contraction rate of the oscillator revealed that its processes dissipative, conservative, and repelled dynamics depending on the values of the bifurcation control parameter. • The mega-stable nature of investigated oscillator is characterized by the coexistence of attractors in a nested structure. • The Hamiltonian-dependence energy is studied to show the mechanism of the megastability. • Multiple coexisting mega-stable attractors are captured in Pspice simulations by configuring initial conditions. Mega-stable oscillators with memristor have not been investigated in the literature up to now. In this contribution, a novel memristive mega-stable oscillator (MMO) with a plethora of properties is introduced. The originality of the introduced systems is that the 3D model exhibits mega-stability without external perturbation, which was not the case in most existing mega-stable models considered in the literature. The investigation of the volume contraction rate of the oscillator revealed that its processes dissipative, conservative, and repelled dynamics depending on the values of the bifurcation control parameter. The mega-stable nature of the investigated oscillator is characterized by the coexistence of attractors in a nested structure. In addition, the well-known Helmholtz theorem is used to determine the Hamiltonian energy used during the mechanism of the megastability. Finally, multiple coexisting mega-stable attractors are captured in Pspice simulations by configuring the initial conditions, further supporting the numerical results. 

Hamiltonian energy computation of a novel memristive mega-stable oscillator (MMO) with dissipative, conservative and repelled dynamics

The present work introduces an analysis framework to comprehend the dynamics of a 3D plasma model, which has been proposed to describe the pellet injection in tokamaks. The analysis of the system reveals the existence of a complex transition from transient chaos to steady periodic behavior. Additionally, without adding any kind of forcing term or controllers, we demonstrate that the system can be changed to become a multi-stable model by injecting more power input. In this regard, we observe that increasing the power input can fluctuate the numerical solution of the system from coexisting symmetric chaotic attractors to the coexistence of infinitely many quasi-periodic attractors. Besides that, complexity analyses based on Sample entropy are conducted, and they show that boosting power input spreads the trajectory to occupy a larger range in the phase space, thus enhancing the time series to be more complex and random. Therefore, our analysis could be important to further understand the dynamics of such models, and it can demonstrate the possibility of applying this system for generating pseudorandom sequences.

https://www.mdpi.com/1099-4300/23/1/48/pdf

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

Multistability and dynamical properties of ion-acoustic flow are studied in a quantum plasma containing positive beam ions, positive ions and electrons. A four dimensional conservative dynamical system has been proposed for the considered plasma system and is analyzed by considering effects of Mach number and quantum diffraction parameter. Coexistences of multiple chaotic trajectories, chaotic with quasiperiodic and multiperiodic trajectories and chaotic with quasi-periodic and periodic trajectories for ion-acoustic waves are established. The results are suitable for application in comprehending the beam-plasma interaction and studying dynamics of coexisting features in extreme astrophysical plasmas, such as, neutron stars.

Multistability and dynamical properties of quantum ion-acoustic flow

Nonlinear dynamical systems with hidden attractors belong to a recent and hot area of research. Such systems can exist in different forms, such as without equilibrium or with a stable equilibrium point. This paper focuses on the dynamics of a new 4D chaotic hyper-jerk system with a unique equilibrium point. It is shown that the new hyper-jerk system effectively exhibits different hidden behaviors, which are hidden point attractor, hidden periodic attractor, and hidden chaotic state. Collective behaviors of the system are studied in terms of the equilibrium point, bifurcation diagrams, phase portraits, frequency spectra, and two-parameter Lyapunov exponents. Some remarkable and exciting properties are found in the new snap system, such as period-doubling transition, asymmetric bubbles, and coexisting bifurcations. Also, we demonstrate that it is possible to generate different varieties of two, three, four, or five coexisting hidden and self-excited attractors in the introduced model. In addition, the amplitude and offset of the hidden chaotic attractors are perfectly controlled for possible application in engineering. Furthermore, a circuit design has been implemented to support the physical feasibility of the proposed model.

Hidden and Self-Excited Collective Dynamics of a New Multistable Hyper-Jerk System with Unique Equilibrium

Based on two of the existing one-dimensional chaotic maps and the two-dimensional Henon map, a new two-dimensional Henon-Gaussian-Sine model (2D-HGSM) is proposed. Basic dynamic characteristics of the 2D-HGSM are studied from the following three aspects: trajectory, bifurcation diagram and Lyapunov exponents. The complexity of 2D-HGSM is investigated by means of Approximate entropy. Performance evaluations show that the 2D-HGSM has higher complexity level, better ergodicity, wider chaotic and hyperchaotic region than different chaotic maps. Furthermore, the 2D-HGSM exhibits a qualitatively different chaotic behavior with respect to the variation of its corresponding parameters. Therefore, the 2D-HGSM has good application prospects in secure communication.

/pdf/complexity-and-dynamic-characteristics-of-a-new-discrete-58ru5wstgp.pdf

Hayder Natiq

Papers

Hamiltonian energy computation of a novel memristive mega-stable oscillator (MMO) with dissipative, conservative and repelled dynamics

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

Multistability and dynamical properties of quantum ion-acoustic flow

Hidden and Self-Excited Collective Dynamics of a New Multistable Hyper-Jerk System with Unique Equilibrium

Complexity and dynamic characteristics of a new discrete-time hyperchaotic model