Chaotic secure communication plays a critical role in ensuring the reliability and robustness of data transmission in the Internet of Things (IoT). Secure communication schemes driven by the multiscroll properties of memristive chaotic systems (MCSs) can enhance security performance. Numerous Multiscroll Memristive Chaotic Systems (MMCSs) have been developed to meet this demand, but most of them rely on nonlinear functions to regulate scroll numbers, resulting in increased complexity and limited applicability. To bridge this gap, this paper proposes a unique memristor model and couples it with a simple Sprott B system to construct a new MMCS, in which the number of scrolls is controlled by a single parameter. Endowed with the nonlinear function of the proposed memristor, the MMCS exhibits rich dynamical behaviors, such as numerous homogeneous and heterogeneous coexisting attractors, controllable partial and full amplitude modulation, and multiscroll offset boosting. Implementation on STM32 hardware also demonstrates that multiscroll structure in the MMCS is governed by a single parameter. Finally, the MMCS is applied to a code division multiple access reference-modulated differential chaos shift keying (DM-RM-DCSK) secure communication scheme, and its performance is validated by experimental results.

To enhance the secure storage and real-time transmission of vehicle images on highways, this study proposes a fast parallel multi-image encryption scheme. First, a dual-memristor exponential map is designed, whose Lyapunov exponents, chaotic attractors, and bifurcation behavior are analyzed, and, based on this, the key stream is used to generate pseudo-random sequences. Subsequently, the acquired multiple vehicle images are subjected to target detection, and all detected vehicle targets are rearranged and divided into blocks. Then, three rounds of parallel diffusion and one round of scrambling operation are applied to the partitioned images, further enhancing plaintext sensitivity and avalanche effect to resist differential attacks. Finally, security analysis shows that the proposed algorithm offers significant advantages in resisting statistical, frequency, entropy, and other common attacks. Moreover, compared with previous studies, it achieves higher encryption speed, averaging 2285.67 KB/s, thus satisfying the security and efficiency requirements for real-time vehicle image data transmission.

This paper presents a dual-key image encryption scheme based on deep neural network. First, a 4D memristive hyperchaotic map is constructed by integrating the Sine map, Logistic map, and a sinusoidal discrete memristor. The resulting map provides high Lyapunov exponents, a broad parameter domain, and an expanded chaotic range, making it suitable for cryptographic applications. On this basis, an image encryption scheme with comprehensive performance enhancements is designed by incorporating SqueezeNet and dual-key mechanism. The proposed scheme maintains a simplified structure while achieving strong performance in security, robustness, and efficiency, and its application in Internet of Things (IoT) environments is illustrated. Simulation and numerical results show that it achieves near-ideal performance in terms of NPCR, UACI, information entropy, and pixel correlation. Additionally, it exhibits strong resistance to high-intensity cropping attacks and multiple types of noise, and requires only 0.1856 s to encrypt a 512×512 color image. These results verify that the scheme ensures a high level of security and reliability in image transmission.

Special tasks in complex and extreme environments require mobile robots to possess the good capabilities of navigation and securing map data. Mobile robots driven by the chaotic properties of memristive neural networks (MNN) can offer intriguing insights. However, the expandable MNN capable of providing multiple reliable options for diverse application scenarios has yet to be thoroughly explored. Hence, this article proposes a new universal method to enhance the dynamics in neural networks for generating numerous neural networks with rich dynamics, providing multiple options for the navigation and security of IoT-based robots. The enhanced dynamics in this method benefit from expanding the number of memristive electromagnetic radiation, the number of neurons, and their integration. Many different memristive central cyclic neural network (MCCNN) are successfully derived from the newly constructed central cyclic neural network as an example. Various dynamics of memristive central cyclic neural networks (MCCNN) are numerically investigated, including bifurcation, homogeneous and heterogeneous multistability, and large-scale amplitude control. The analog circuit and digital hardware platform are built to verify the physical existence and feasibility of MCCNN. Finally, MCCNN is applied to drive the IoT-based mobile robot. To evaluate the robot's area coverage, obstacle avoidance performance, several experiments are carried out, which validate the robot's superiority.

Constructing memristive neural networks (MNNs) with multiscroll chaotic attractors helps advance both theoretical and applied research on neural networks. However, the existing models mainly utilize complex memristor models with polynomial functions, nested composite functions, and so on, to generate multiscroll chaotic attractors, which leads to increased model complexity and difficulties in on-demand adjustment. Hence, this article proposes a reconfigurable multiscroll MNN (RMMNN) that can yield different types of multiscroll chaotic attractors merely by altering the memristive parameters without modifying its model. Through numerical methods, the complex dynamics of the RMMNN in different cases are analyzed, such as parameter-controlled multiscroll chaotic attractors, adjustable multistability, and parameter-induced transitions of multistability. In addition, the reliability of the numerical analysis is verified via the hardware circuits. Moreover, to address the issues of image security and low quality in telemedicine, a bidirectional rotation medical image encryption scheme (BRMIES) is developed based on the good pseudorandom chaotic sequences generated by RMMNN. Performance analysis demonstrates that BRMIES can effectively protect medical image and robustly handle various potential adverse interferences within telemedicine process.

In recent years, network attacks on medical information have posed a significant threat to the development of the Internet of Medical Things (IoMT). To address these threats, this paper proposes a novel chaos-based encryption scheme for 3D medical models. First, a new memristive hyperchaotic map (LC-CMHM) is designed. Simulation results demonstrate that, compared to classical chaotic maps, LC-CMHM exhibits stronger ergodicity and unpredictability, ensuring security for the encryption algorithm. Additionally, hardware implementation verifies its feasibility. Utilizing pseudo-random numbers generated by LC-CMHM, a tailored encryption algorithm is developed specifically for the structural features of 3D medical models. This algorithm encrypts both the faces and vertices of the 3D model, disrupting inherent correlations to enhance encryption effectiveness. Performance analysis confirms that the proposed scheme effectively transforms meaningful 3D medical data into a chaotic, unrecognizable sequence, providing strong resistance against differential attacks, chosen-plaintext attacks, and statistical attacks.

An innovative lightweight image encryption scheme with superior security performance has been developed. Initially, we construct a 3-D simple memristive hyperchaotic map (3-D-SMHM) that exhibits remarkable hyperchaotic characteristics within a simple structure. Through comprehensive analysis of its performance metrics, the map reveals excellent unpredictability and ergodicity, providing a solid foundation for encryption applications. Utilizing the 3-D-SMHM, we introduce a novel colliding parity lightweight image encryption scheme (CPL-IES), which uniquely integrates a scrambling mechanism based on the collision principle with a diffusion strategy relying on parity. After comprehensive verification through seven experiments, CPL-IES demonstrates outstanding performance in terms of efficiency, robustness, and security, making it suitable for application in resource-constrained devices but stringent security requirements.

Traditional low dimensional chaotic maps suffer from limited dynamical complexity and weak randomness, reducing their effectiveness in applications. This paper presents a general framework for constructing 4-D memristive hyperchaotic maps, from which four representative hyperchaotic maps are developed. These maps exhibit diverse dynamical behaviors. Importantly, all four maps are designed without fixed points due to the inclusion of two oscillatory terms. By adjusting the internal memristor state, they generate infinitely many coexisting attractors, and they further enable controllable amplitude modulation as well as parameters driven attractors offset boosting. A digital hardware platform is developed to implement the proposed maps and experimental results demonstrate their robustness and feasibility in embedded environments. An image encryption algorithm based on it is designed, results exhibiting robust resistance against brute-force attacks, diverse noise attacks at varying intensities, cropping attacks and differential cryptanalysis.

With consideration of the inherent nonlinearity and distinctive memory characteristics, memristors are excellent candidates for constructing multiscroll attractors. This paper seeks to introduce a memristor into the Chua’s circuit to operate in conjunction with a novel piecewise nonlinear resistor which replaces the Chua’s diode to design the circuit that can generate grid multiscroll attractors, which is designated as multiscroll memristive Chua’s circuit (MMCC). The designed MMCC is capable of generating any number of scrolls, with the number of scrolls expanding in accordance with the internal variables of the memristor and the nonlinear resistor. By utilizing phase portraits, bifurcation diagrams, Lyapunov exponents (LEs), coexisting attractors and amplitude modulation thoroughly examined its property. The feasibility of the MMCC is demonstrated through circuit implementation. Furthermore, we design the predefined-time synchronization (PTS) controller for the MMCC, serving as the foundation for a multi-channel segmented secure communication scheme, whose effectiveness is rigorously validated through experimental testing.

Medical images exhibit a wide range of gray scales and are frequently affected by noise and artifacts, necessitating high security and robustness during transmission. A novel medical image encryption scheme combined with compressed sensing is proposed. This scheme utilizes the reconstructed hyperchaotic map as tool for generating random sequences. Through multi-faceted dynamic behavior analysis of the map, it has been verified that it possesses excellent unpredictability and an ultra-wide key space, as well as its hardware implementation lays a foundation for practical image encryption. By decomposing the image into bit-planes, cross scrambling and ascending diffusion are applied to different bit-planes. Combined with compressed sensing, the medical image is transformed into ciphers of varying sizes to achieve the purpose of secure transmission. This approach significantly enhances encryption efficiency by reducing image size. Comprehensive multi-dimensional performance tests demonstrate its superior effectiveness in medical image encryption, providing strong security performance for the application of the scheme in the Internet of Medical Things (IoMT).

Due to their synaptic-like characteristics and memory properties, memristors are often used in neuromorphic circuits, particularly neural network circuits. However, most of the existing neural network circuits that can generate complex dynamics have high dimensions and excessive connections, which is not conducive to implementation. This article introduces a memristor containing an arctangent function into a simple cyclic neural network (SCNN) circuit to design a simple cyclic memristive neural network (SCMNN) circuit capable of generating complex multiscroll chaotic attractors. The designed SCMNN contains an external stimulus current and generates multiscroll attractors, with the number of scrolls expanding as the switches in the memristor equivalent circuit are activated. By varying the parameters, the multiscroll attractors can be broken into different numbers of coexisting attractors, which also depends on the switch, and it can achieve multivariable amplitude control when there is only one scroll. The anti-interference ability of the circuit is tested. A low-cost circuit-based microcontroller suitable for engineering applications is designed for it, and multiscroll attractors are successfully captured in an oscilloscope. The National Institute of Standards and Technology (NIST) test is carried out to verify its application value.

The security of a chaos-based image encryption (IE) systems is based upon chaotic map’s performance and the encryption algorithm’s permutation and diffusion strategies. Nevertheless, existing IE schemes exhibit different drawbacks, such as limited disordering capabilities, inadequate dynamic performance, and the chaotic maps’ insensitivity. To address these limitations, this study presents an octal-based shuffling and multilayer rotational diffusing IE (OSMRD-IE) utilizing a 2-D hybrid Michalewicz–Ackley (2-D-HMA) map. The 2-D-HMA map has the capability to generate new hyperchaotic maps by integrating hybrid functions using different encapsulation functions. The integration of a map generator could lead to dynamic nature, chaotic perturbations, and parameter control mechanisms. To enhance the algorithm’s resilience against cyberthreats, the 2-D-HMA map-based OSMRD-IE scheme shuffles the pixels using octal-base scrambling and manipulates pixel values through multilayer rotation. By means of comparisons with existing techniques, the OSMRD-IE scheme’s reliability and 2-D-HMA map’s dynamic performance are validated independently. The superior chaotic properties of the 2-D-HMA map are evident in the experimental results, establishing OSMRD-IE as the more reliable scheme in both visual and quantitative comparisons.

In view of the superiority of memristors in strengthening dynamical complexity and the significant application potiential of multiscroll chaos, this paper attempts to introduce two memristors with scalable memductances into simple seed chaotic system for designing multiscroll memristive chaotic system (MMCS). The designed MMCS yields hidden grid multiscroll chaotic attractors with any number of scrolls expanding along with the internal variables of memristors. By varying the parameters, the multiscroll attractors can be broken into coexisting attractors with different numbers and scrolls dependent on parameters, and their oscillation amplitudes can be increased (or decreased) without changing the chaotic features. Dynamical analysis and circuit implementation are given to reveal the complexity and feasibility of the MMCS. The fixed-time synchronization (FxTS) is studied by using adaptive controller and the sufficient condition for FxTS is established via Lyapunov stability theory (LST). A multilevel secure communication scheme based on the FxTS of MMCS is designed and the experimental tests on the image, audio and data secure communication verify its effectiveness, which to some extent shows the application availability of MMCS.

Memristor possesses synapse-like properties that can mimic excitation and inhibition between neurons. This article introduces the Sigmoid functions to the memristor and constructs a new memristive Hopfield neural network (HNN). Its most distinctive feature is the simple topology, which contains only unidirectional connections in neurons. The equilibrium points analysis reveals the mechanism of its multiscroll attractors generation. Homogeneous and heterogeneous coexisting attractors are observed with the variation of the network parameters. Note that the state equation of memristor can affect the number of coexisting attractors. A hardware implementation is designed for it, and the multiscroll attractors are captured in the oscilloscope. Finally, it is also applied to developing an image encryption algorithm with excellent performance.

Medical image encryption is a crucial technique to safeguard patient privacy and medical information security. This article proposes a novel medical image encryption scheme that combines compressive sensing techniques based on the designed memristive hyperchaotic system. Unlike traditional encryption methods that make it hard to handle large volume of data like medical images, the proposed scheme can quickly encrypt a large volume of medical images into a cipher image of a custom size, which greatly increases the efficiency of the algorithm. The security performance of the proposed algorithm is evaluated and analyzed in detail. Experimental results show that NPCR and UACI values are closer to 99.60% and 33.46%, the encryption speed can reach 1860.47 kb$/$s, which outperforms traditional methods. This work provides a new research method for the encryption of medical images and has important significance in the Internet of Medical Things (IoMT).

A chaotic system is a mathematical model exhibiting random and unpredictable behavior. However, existing chaotic systems suffer from suboptimal parameters regarding chaotic indicators. In this study, a novel leader Pareto grey wolf optimizer (LP-GWO) is proposed for multiobjective (MO) design of 2D parametric hyperchaotic system (2D-PHS). The MO capability of LP-GWO is improved by integrating a LP solution within the Pareto optimal set. The effectiveness of LP-GWO is corroborated through a comparison with regular MO versions of grey wolf optimizer (GWO), artificial bee colony, particle swarm optimization, and differential evolution. Additionally, the validation extends to the exploration of LP-GWO’s performance across four variants of the 2D-PHS optimized by the compared algorithms. A 2D-PHS model with eight parameters is conceived and then optimized using LP-GWO by ensuring tradeoff between two objectives: Lyapunov exponent (LE) and Kolmogorov entropy (KE). A globally optimal design is chosen for freely improving the two objectives. The chaotic performance of 2D-PHS significantly outperforms existing systems in terms of precise chaos indicators. Therefore, the 2D-PHS has the best ergodicity and erraticity due to optimal parameters provided by LP-GWO.

Memristors are well suited as artificial nerve synapses owing to its unique memory function. This paper establishes a novel flux-controlled memristor model using hyperbolic function series. By taking the memristor as synapses in a Hopfield neural network (HNN), three memristive HNNs are constructed. These memristive HNNs can generate multi-double-scroll chaotic attractors or grid multi-double-scroll chaotic attractors. The number of double scrolls in the attractors is controlled by the memristor. Equilibrium points analysis further reveals the generation mechanism of grid multi-double-scroll chaotic attractors. Moreover, numerical simulations indicate the existence of complex dynamics in the memristive HNNs, including extreme multistability and amplitude control. An approach to physically realize grid multi-double-scroll chaotic attractors is also given. Finally, an encryption scheme based on the proposed memristive HNN is designed to demonstrate application potential of the attractors.

Due to complex chaotic characteristics and multistable states, the generation of multi-wing hidden chaotic attractors shows a new application prospect in chaos-based security communication. However, for chaotic systems with multiple stable equilibria, the point attractors have attraction basins that are separately embedded in the initial value space, which makes it difficult to generating bands to connect different wings or scrolls. Up to now, grid-wing hidden chaotic attractors with only stable equilibria have not been reported yet. In this paper, a novel system for generating symmetric and asymmetric hidden chaotic attractors is proposed. By applying symmetric piecewise-linear modulation functions to a seed system with only two stable equilibria, multiple stable equilibria with single-direction pair distribution and two-direction grid distribution are configured. Principle of the key technique is based on the offset switch, which effectively connect different wings via the switch bands. Consequently, multi-wing, multi-double-wing, and grid-wing hidden chaotic attractors are generated. Besides, applying asymmetric modulation functions lead to the generation of asymmetric multi-wing hidden chaotic attractor. Attraction basins of various multi-wing and grid-wing hidden attractors are investigated to show the multistability. Numerical simulations and corresponding FPGA-based physical experiments validated the feasibility of the generation method.

Conventional amplitude versus offset (AVO) inversion methods are mainly based on various Zoeppritz approximations. The assumptions of small contrast and linear relationship lead to the most inversion methods being difficult to have high inversion accuracy. In this article, the exact Zoeppritz equation is used to establish the prestack inversion method under the Bayesian framework. It integrates multisource information to generate posterior distributions of P-, S-wave velocity and density. In the Bayesian theory, the prior model works as the regularization term which has a strong effect on the inversion results. The strategy to obtain a relatively accurate prior model can improve the inversion accuracy. Therefore, an exact Zoeppritz equation based nonlinear AVO inversion algorithm combing whale optimization particle filtering (WOPF) is proposed. The WOPF method can generate a relatively stable and accurate initial model for the Bayesian prestack inversion. We validate the new method through two synthetic models and field data. Comparisons are made with the conventional linear and nonlinear AVO inversion methods. The results show that the proposed method can provide much more accurate inverted elastic parameters in different geological conditions.

Memristor is an ideal electronic device used as an artificial nerve synapse due to its unique memory function. This article presents a design of a new Hopfield neural network (HNN) that can generate multiscroll attractors by utilizing a new memristor as a synapse in the HNN. Differing from the others, this memristor is constructed with hyperbolic tangent functions. Taking the memristor as a self-feedback synapse of a neuron in the HNN, the memristive HNN can yield multidouble-scroll attractors, and its parameters can be used to effectively control the number of double scrolls contained in an attractor. Interestingly, the generation of multidouble-scroll attractors is independent of the memductance function but depends only on the internal state equation. Thus, the memductance function can be adjusted to yield various complex dynamical behaviors. Moreover, amplitude control effects and quantitatively controllable multistability are revealed by numerical analysis. The accurate reproduction of some dynamical behaviors by a designed circuit verifies the correctness of the numerical analysis. Finally, based on the proposed memristive HNN, a novel image encryption scheme in the 3-D setting is designed and evaluated, demonstrating its good encryption performances.

This paper is concerned with the consensus tracking problem for heterogeneous interdependent group systems with fixed communication topologies. First, the interdependent model of the heterogeneous system is built from the perspective of the difference of the individual characteristic and the difference of the subgroup topology structure. A class of distributed consensus tracking control protocol is proposed for realizing the consensus tracking of the heterogeneous interdependent group system via using local information. Then, for fixed communication topologies, some corresponding sufficient conditions are given to ensure the achievement of the consensus tracking. Two parameters are defined, which denote, respectively, the proportion of interdependence individual and the redundancy of interdependence. The effects of these parameters are analyzed on the consensus tracking of group systems. Numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

In this paper, the flocking behavior and targets consensus tracking problems of heterogeneous multiple inertial agents with limited communication ranges are investigated. Consider the inertial effect of real agents, a distributed control protocol is designed such that the agents can achieve stable group behaviors. Using the decomposition approach, the stability of a multiple inertial agents system is proved. Combining with the flocking behavior of multiple inertial agents, agents themselves are in charge of searching and choosing the target in an autonomous and individual way according to the relationship between velocities of agents and targets. An augmented distributed multiflocking method is proposed to guarantee that the multitarget consensus tracking can be reached for heterogeneous multiagent systems. It shows that the proposed control approach can not only ensure local flocking with pursuing agents, but also make heterogeneous agents consistently track the multitarget.