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This paper presents a new method for constructing N-dimensional discrete sine hyperchaotic maps (NSHMs). This method can efficiently generate different hyperchaotic maps with arbitrary dimensions by designing different seed functions and different system dimensions. By this method, we constructed three different sub-maps, namely a 2-dimensional discrete sine hyperchaotic map (2SHM), a 4-dimensional discrete sine hyperchaotic map (4SHM) and a 6-dimensional discrete sine hyperchaotic map (6SHM). These three sub-maps not only have simple structures, but also possess complex dynamical behaviors, such as initial-boosting behaviors, large Lyapunov exponents (LLEs), and ultra-wide non-degenerate hyperchaotic parameter range (UHPR). In addition, we also conducted spectral entropy (SE) complexity analysis and National Institute of Standards and Technology (NIST) tests on these three sub-maps. Finally, the three sub-maps were implemented using the STM32 hardware platform.

The continuous memristor is a popular topic of research in recent years, however, there is rare discussion about the discrete memristor model, especially the locally active discrete memristor model. This paper proposes a locally active discrete memristor model for the first time and proves the three fingerprints characteristics of this model according to the definition of generalized memristor. A novel hyperchaotic map is constructed by coupling the discrete memristor with a two-dimensional generalized square map. The dynamical behaviors are analyzed with attractor phase diagram, bifurcation diagram, Lyapunov exponent spectrum, and dynamic behavior distribution diagram. Numerical simulation analysis shows that there is significant improvement in the hyperchaotic area, the quasi periodic area and the chaotic complexity of the two-dimensional map when applying the locally active discrete memristor. In addition, antimonotonicity and transient chaos behaviors of system are reported. In particular, the coexisting attractors can be observed in this discrete memristive system, resulting from the different initial values of the memristor. Results of theoretical analysis are well verified with hardware experimental measurements. This paper lays a great foundation for future analysis and engineering application of the discrete memristor and relevant the study of other hyperchaotic maps.

Chaos-based cryptology has become one of the most common design techniques to design new encryption algorithms in the last two decades. However, many proposals have been observed to be weak against simple known attacks. However, security of proposals cannot be proved. An analysis roadmap is needed for the security analysis of new proposals. This study aims to address this shortcoming. Analysis and test results show that many chaos-based image encryption algorithms previously published in the nonlinear dynamics are actually not as secure as they are expressed although these algorithms do pass several statistical and randomness tests. A checklist has been proposed to solve these problems. The applications of the proposed checklist have been shown for different algorithms. The proposed checklist is thought to be a good starting point for researchers who are considering to work in chaos-based cryptography.

Neural networks are favored by academia and industry because of their diversity of dynamics. However, it is difficult for ring neural networks to generate complex dynamical behaviors due to their special structure. In this paper, we present a memristive ring neural network (MRNN) with four neurons and one non-ideal flux-controlled memristor. The memristor is used to describe the effect of external electromagnetic radiation on neurons. The chaotic dynamics of the MRNN is investigated in detail by employing phase portraits, bifurcation diagrams, Lyapunov exponents and attraction basins. Research results show that the MRNN not only can generate abundant chaotic and hyperchaotic attractors but also exhibits complex multistability dynamics. Meanwhile, an analog MRNN circuit is experimentally implemented to verify the numerical simulation results. Moreover, a medical image encryption scheme is constructed based on the MRNN from a perspective of practical engineering application. Performance evaluations demonstrate that the proposed medical image cryptosystem has several advantages in terms of keyspace, information entropy and key sensitivity, compared with cryptosystems based on other chaotic systems. Finally, hardware experiment using the field-programmable gate array (FPGA) is carried out to verify the designed cryptosystem.

Secure image encryption is critical for protecting sensitive data such as satellite imagery, which is pivotal for national security and environmental monitoring. However, existing encryption methods often face challenges such as vulnerability to traffic analysis, limited randomness, and insufficient resistance to attacks. To address these gaps, this article proposes a novel multiple image encryption (MIE) algorithm that integrates hyperchaotic systems, Singular Value Decomposition (SVD), counter mode RC5, a chaos-based Hill cipher, and a custom S-box generated via a modified Blum Blum Shub (BBS) algorithm. The proposed MIE algorithm begins by merging multiple satellite images into an augmented image, enhancing security against traffic analysis. The encryption process splits the colored image into RGB channels, with each channel undergoing four stages: additive confusion using a memristor hyperchaotic key transformed by SVD, RC5 encryption in counter mode with XOR operations, Hill cipher encryption using a 6D hyperchaotic key and invertible matrices mod 256, and substitution with a custom S-box generated by a modified BBS. Experimental results demonstrate the proposed algorithm’s superior encryption efficiency, enhanced randomness, and strong resistance to cryptanalytic, differential, and brute-force attacks. These findings highlight the MIE algorithm’s potential for securing satellite imagery in real-time applications, ensuring confidentiality and robustness against modern security threats.

Biological nervous system function is closely related to its dynamical behaviors, and some dynamical phenomena observed in biological systems can be detected in the simplified neural models. In this paper, the chaotic dynamics in a three-neuron-based Hopfield neural network (HNN) with stimulation of electromagnetic radiation is investigated. The neural network is modeled by utilizing a flux-controlled memristor to describe the effects of electromagnetic field on neurons. The simple neural model affected by electromagnetic radiation does not contain any equilibrium points, but can induce coexisting infinitely many hidden attractors, such as hyperchaos, transient hyperchaos, period, quasi-period, chaos as well as transient chaos with different chaotic times. In particular, the dynamics of hidden extreme multistability with hyperchaos and transient chaos in the neural network highly depends on the system parameters and state initial values. The coexistence of multiple hidden attractors is revealed via applying a host of numerical analysis methods including phase plots, time sequence waveforms, bifurcation diagrams, Lyapunov exponents and attraction basins. Besides, a HNN-based circuit consisting of commercially available electronic elements is designed to verify the theoretical analysis. Hardware measurement and MULTISIM simulation results are basically consistent with MATLAB numerical simulation results.

Memristor is a nonlinear electronic component with good plasticity, and it is widely used to function as the synapse. Significantly, the inter-neuronal communication is a discrete process via neurotransmitter, and the discrete memristor is suitable to emulate its dynamics. With the introduction of discrete memristors, the discrete neural models coupled with memristors have received widespread attention. In this paper, we present a one-dimensional (1D) Chialvo map, and a discrete memristor-coupled Chialvo neuron (DMCCN) map is designed by bidirectionally coupling two 1D Chialvo maps through a discrete memristor. The DMCCN map exhibits a linear fixed point set dependent on the initial condition of the memristor, and the stability is discussed. The dynamical behaviors are investigated through Lyapunov exponents (LEs), bifurcation diagrams, phase portraits, and firing patterns. The results indicate that the DMCCN map generates complex dynamical behaviors, such as chaos, hyperchaos and coexisting firing patterns. Specifically, these behaviors are highly dependent on the initial conditions, leading to initial-induced heterogeneous multistability and initial-boosted homogeneous multistability. Furthermore, a hardware circuit based on the DSP platform is designed to implement the DMCCN map, verifying its application potential.

In this paper, the hyperchaos analysis, optimal control, and synchronization of a nonautonomous cardiac conduction system are investigated. We mainly analyze, control, and synchronize the associated hyperchaotic behaviors using several approaches. More specifically, the related nonlinear mathematical model is firstly introduced in the forms of both integer- and fractional-order differential equations. Then the related hyperchaotic attractors and phase portraits are analyzed. Next, effectual optimal control approaches are applied to the integer- and fractional-order cases in order to overcome the obnoxious hyperchaotic performance. In addition, two identical hyperchaotic oscillators are synchronized via an adaptive control scheme and an active controller for the integer- and fractional-order mathematical models, respectively. Simulation results confirm that the new nonlinear fractional model shows a more flexible behavior than its classical counterpart due to its memory effects. Numerical results are also justified theoretically, and computational experiments illustrate the efficacy of the proposed control and synchronization strategies.

This paper describes a novel 4-D hyperchaotic system with a high level of complexity. It can produce chaotic, hyperchaotic, periodic, and quasi-periodic behaviors by adjusting its parameters. The study showed that the new system experienced the famous dynamical property of multistability. It can exhibit different coexisting attractors for the same parameter values. Furthermore, by using Lyapunov exponents, bifurcation diagram, equilibrium points’ stability, dissipativity, and phase plots, the study was able to investigate the dynamical features of the proposed system. The mathematical model’s feasibility is proved by applying the corresponding electronic circuit using Multisim software. The study also reveals an interesting and special feature of the system’s offset boosting control. Therefore, the new 4D system is very desirable to use in Chaos-based applications due to its hyperchaotic behavior, multistability, offset boosting property, and easily implementable electronic circuit. Then, the study presents a voice encryption scheme that employs the characteristics of the proposed hyperchaotic system to encrypt a voice signal. The new encryption system is implemented on MATLAB (R2023) to simulate the research findings. Numerous tests are used to measure the efficiency of the developed encryption system against attacks, such as histogram analysis, percent residual deviation (PRD), signal-to-noise ratio (SNR), correlation coefficient (cc), key sensitivity, and NIST randomness test. The simulation findings show how effective our proposed encryption system is and how resilient it is to different cryptographic assaults.

This paper studies a four-dimensional (4D) memristive system modified from the 3D chaotic system proposed by Lü and Chen. The new system keeps the symmetry and dissipativity of the original system and has an uncountable infinite number of stable and unstable equilibria. By varying the strength of the memristor, we find rich complex dynamics, such as limit cycles, torus, chaos, and hyperchaos, which can peacefully coexist with the stable equilibria. To explain such coexistence, we compute the unstable manifolds of the equilibria, find that the manifolds create a safe zone for the hyperchaotic attractor, and also find many heteroclinic orbits. To verify the existence of hyperchaos in the 4D memristive circuit, we carry out a computer-assisted proof via a topological horseshoe with two-directional expansions, as well as a circuit experiment on oscilloscope views.