The multiscroll chaotic system, with its complex phase space topology, offers broad applicability in real-time path planning for the Internet of Things (IoT). In this work, it is found that the combination of attractor doubling can help to reconstruct or even strengthen the bidirectional bonding strap, and thus cooperate with the dynamics editing for building and reshaping any desired multiscroll topological structure. From this routine, 2-D or 3-D controlled multiscroll attractors can be produced, in which the technology of attractor doubling and dynamics editing can be combined in a flexible strategy, and thus the multiscroll attractors present richer embedded forms. Additionally, the proposed concepts of convergence fields and switching regions provide a new analytical perspective for understanding multiscroll structures. FPGA-based hardware experiments successfully verify the feasibility of implementing such systems on embedded platforms. Test results indicate that integrating the Pelican Optimization Algorithm (POA) with the multiscroll system yields an average performance improvement of approximately 5%.

This research focuses on improving the transistor-based fractional exponentiation circuit (also known as 444 circuit). It aims to address the issue of insufficient stability and verifies the adaptability of the chaotic system through hardware experiments. Starting from three feedback capacitors as the improvement point, mathematical modeling analysis and circuit simulation verification effectively improve the system’s bandwidth and dynamic response characteristics. The optimized circuit is embedded in the VB5 system, constructing a series of chaotic systems with nonlinear feedback. The chaotic phase trajectories obtained from experimental observations are highly consistent with the theoretical predictions, providing key empirical evidence for the improvement of the stability of the 444 circuit. This research achievement opens up a low-cost technical implementation path for the realization of complex nonlinear feedback, such as fractional exponent operation in chaotic circuits.

The Hopfield neural network with unidirectional fixed resistance weights has been shown to exhibit limited complex dynamical behaviors due to its relatively simple architecture. To address this limitation, this paper proposes a new tri-memristor hyperchaotic ring neural network (THRNN). The THRNN facilitates the generation of hidden chaos and demonstrates homogeneous/heterogeneous multistability. Homogeneous coexisting attractors, when tightly connected across barriers, exhibit significant self-growth behavior over time. The number of growth directions can be freely regulated, and the multidirectional initial offset boosting characteristics of these growing attractors can also be readily observed. Furthermore, abundant hidden firing patterns are well-tuned by the coupling parameters of the memristors, resulting in chaotic bursting firing, periodic bursting firing, chaotic spiking firing, and periodic spiking firing. Particularly, a more complicated hidden hyperchaotic firing pattern is also discovered and captured. Moreover, an STM32H7 digital circuit is built to verify the findings presented in this paper. Finally, a hardware image blocking encryption system based on FPGA and the THRNN is proposed. This encryption system constructs a framework based on the hyperchaotic firing attractors and homogeneous multistability attractors. It realizes dynamic key update through block encryption strategy, and completes key scrambling by combining Cat mapping and sequence sorting, which significantly enhances encryption security. Relying on FPGA hardware implementation, its parallel processing capability greatly improves encryption efficiency, and the hardware deployment feature enhances the system’s stability and practicality, providing an efficient solution for high-security image encryption.

In practical applications, effectively regulating the amplitude of chaotic signals and maintaining the chaotic nature of the system are extremely critical to ensure system stability and prevent failures. However, traditional amplitude control methods usually change the bifurcation threshold or attractor geometry, impairing the integrity of chaos and increasing the risk of system instability, thus struggling to achieve effective control over complex chaotic signals. Given the rapid advancement in brain-inspired intelligence technology, it has become imperative to investigate new control techniques based on memristors to overcome the limitations of conventional approaches. To address these challenges, in this paper, a novel dual memristor-coupled Hopfield Neural Network (DMCHNN) is established, where one memristor represents external electromagnetic radiation and the other mimics synaptic connections. Two independent amplitude controllers are devised for signal rescaling, being capable of adjusting signal amplitudes in various modes, such as single-scroll, double-scroll, multi-double-scroll and coexisting homogeneous multi-scroll attractors induced by initial offset boosting. Simulations indicate that the parameter operating range of the amplitude controllers can reach up to 105or beyond. Furthermore, the performance of the amplitude controllers is additionally verified through the implementation based on the CH32 microcontroller. Rescaled chaotic signals are evaluated to determine their robust effectiveness in the deployment of pseudo-random number generators (PRNG). Eventually, the multi-scroll chaotic data with different amplitudes generated from DMCHNN is fed into the optimization algorithms for neural network optimization, which is utilized for medical image classification.

By designing a proper electromagnetic constraint within a memristor, and introducing it into a dynamical system with the increase of dimension, a class of memristive chaotic systems with 2-D offset boosters is constructed. One offset constant directly applies offset boosting of a system variable while the other modifies the offset of two variables simultaneously. Furthermore, when the derived structure satisfies a specific feedback balance law, the property of total amplitude control can be obtained. The circuit implementation is consequently realized and the results are in line with the theoretical analysis.

Memristors have been widely integrated into neurons as the bridge for introducing external magnetic induction currents. The complex oscillation induced by the external magnetic stimulation is a hot topic in neuron dynamics. When a memristor is introduced into the Hindmarsh-Rose (HR) neuron to simulate the external magnetic field, a novel memristive neuromorphic hyperchaotic oscillator is constructed. The memristor weight can trigger complex neuronal firing dynamics, including the rare hyperchaotic bursting. Furthermore, when the technology of offset boosting-oriented attractor doubling is employed, a double-scroll hyperchaotic attractor can be generated, which could split into three independent coexisting attractors under some specific offsets. More interesting, two symmetric periodic attractors and two symmetric hyperchaotic attractors can coexist under certain conditions. In this work, a neuron with coexisting hyperchaotic attractors is constructed and exhaustively explored, which provides a good candidate for constituting large-scale brain-like neuromorphic oscillator. A PCB-based hardware circuit produces the oscillations validating the numerical simulations and theoretical analyses.

Chaotic behavior can be improved through specific types of nonlinear feedback, thereby offering profound insights into chaos control. In this work, a class of nonlinear functions is utilized as feedback to explore the various dynamics of amplitude regulation in the modified 3D Rulkov neurons, thereby changing its brain-like firing patterns. Three different functions are embedded in Rulkov neurons for the outcome of complex dynamics, including the amplitude and frequency control of firing oscillation. Specifically, the pumping effect from a neuron parameter is analyzed, where the energy and amplitude of the firing are almost linearly rescaled by the input acting as a pivotal element for enhancing the transmission of neural signals. Furthermore, when the nonlinear feedback is obtained from a periodic function, coexisting double-scroll phase orbits induced by the initially-controlled offset boosting are arranged in phase space with the same shape and different amplitude. Finally, the digital circuit implemented by CH32 is carried out to verify complex firings. The Pseudo-Random Number Generator is employed as the technology to show the complexity of chaotic firing.

The static architecture of artificial neural networks has fixed synaptic weights, whose connections do not change according to new information or learning experience. In contrast, the capacity of synaptic weight empowers biological neural networks to learn and adapt to diverse tasks, resulting in various dynamical behaviors. In this paper, a novel memristor model is designed into the Hopfield neural network for generating any desired number of multi-scroll attractors. Offset booster provides a channel for distance regulation and number control of coexisting attractors. Independent offset boosters determine the coexisting patterns including the types of one-scroll attractor, two-scroll attractor, four-scroll attractor, and other mixed types. In addition, the digital circuit platform of CH32V307 is applied to verify numerical simulations. Finally, the chaotic data generated in the memristive Hopfield neural network is introduced into the northern goshawk optimization (MHNN-NGO), by which the full network optimization is achieved.

Evidences have manifested that unidirectional ring neural networks lack the ability to generate desired chaos. This paper formulates a novel memristor regulation (MR) approach to constructing a no-equilibrium bi-memristor unidirectional ring neural network (BMURNN), in which two distinct memristors are incorporated into a unidirectional ring neural network derived from the Hopfield neural network, with enhanced chaotic complexity, whereas one serving as a memristive synapse and the other as an emitter of electromagnetic radiation. Numerical simulations reveal that any desired number of multi-scroll hidden chaotic attractors can be generated from the BMURNN via the non-ideal multi-piecewise nonlinear memristor, while the time-controlled multi-scroll attractor growth is output from the periodic function memristor, demonstrating that the memristors can enhance the chaos complexity of the original unidirectional ring neural network. Additionally, diverse coexisting hidden attractors, that is, hidden heterogeneous/homogeneous multistability evoked by the memory attributes of memristors, can be dynamically regulated by varying the initial conditions. Finally, a digital circuit is designed and implemented based on CH32 to validate the numerical simulations and theoretical analyses, and a new pseudorandom number generator is devised to explore the BMURNN for practical applications. Performance analyses demonstrate its superiority and high randomness, providing further proof for the effectiveness of the proposed MR method.

A phase-shifting chaotic oscillator is constructed by memristive coupling. The introduced memristor revises the frequency response as the core of the frequency selection network in the oscillator. A controlled memristor is derived to maintain a stable amplification. Thus, the oscillator has two independent offset boosting voltages, and the voltages of two capacitors can be effectively controlled by cancellation. More conveniently, the simultaneous and proportional change of the op-amp supply voltage and the memristor in the oscillator also rescales the capacitors’ voltages in the same proportion. Finally, a memristor-equivalent circuit with the feedback from AD633 for division operation greatly reduces the cost of components. The hardware experiment confirms the theoretical analysis and numerical simulations.

Memristors have been extensively studied in the field of nonlinear dynamics. However, the dynamic regulation mechanism of memristor-induced hyperchaotic oscillation has not been focused. In this article, a 5-D memristive hyperchaotic oscillator with amplitude control and uncountably many attractors reflecting the arbitrary relocation of the dynamics is constructed and analyzed. In this system, one parameter embedded in the memristor is responsible for partial amplitude control. An independent constant is applied for offset boosting with two system variables. Also, variable boosting can be achieved by varying the initial values, indicating that the system has homogenous multistability, which is shown to have uncountably many continuously distributed attractors. This memristive system provides the first example with uncountably many coexisting hyperchaotic attractors without any periodic function involved. Circuit implementation verifies the theoretical analysis and numerical simulations. A manganese electrolysis experiment was proposed to verify the unique advantage of offset-controllable hyperchaotic current in industrial electrolysis.

Signum and absolute value functions show great potential in chaos generation. Aiming to design an easy-to-use non-smooth circuit component, a Triode-based Analog Gate (TAG) is designed, which consists of only one triode, two op-amps and four resistors for analog signal selection. By choosing external resistors and signals, TAG can be easily extended to absolute value circuit, scalar multiplication circuit, analog selector-mixed subtraction circuit, sum signal selector circuit and piecewise selector circuit. The importance of this class of circuit modules is intensified by its low cost, high accuracy, easy integration and expansion. In this report, a hyperchaotic circuit, a circuit for attractor doubling and multi-scroll generation are consequently designed based on TAG circuits showing their great flexibility and extendibility.

As the bounds of convergence time (CT) for fixed-time (FxT) stability have connections with some parameters of the system, the existing methods of FxT stability are still not really FxT. Therefore, this article studies FxT synchronization of complex networks (CNs) by proposing a new FxT stability theorem. First, the new FxT stability theorem is proposed, the CT of the system is any given time in advance, which is not concerning the starting value and parameters of the system. Second, a set of new controllers, including the continuous controller (CCr) and discontinuous controller (DCCr) are, respectively, designed to obtain the new FxT synchronization criteria for the CNs. Moreover, the control methods effectively solve the CT boundary problem associated with the system parameters in the previous FxT stability methods. Finally, numerical simulations and analog circuits are used to verify the effectiveness of the discussed method.

Two generalized flux-controlled memristors are applied for hyperchaos generation, and following a four-dimensional hyperchaotic oscillator is constructed. The applied two memristors share a common internal control variable. The new hyperchaotic oscillator exhibits complex dynamics including coexisting chaos and attractor merging. A single constant can realize offset boosting revising the oscillation distribution in phase space. Meanwhile, an amplitude knob rescales the variable making it convenient to construct an analog circuit. The implementation of an analog circuit verifies the consistency with numerical simulation and theoretical analysis.

Memristors are widely used to construct multi-scroll/wing chaotic systems with complex dynamics. However, the generation of a multi-scroll/wing attractor is typically not induced by the memristor but depends on other nonlinear functions in the system, which does not take advantage of the unique features of the memristor for chaos-based applications. To address this issue, the present paper introduces a memristor coupling (MC) method to construct a novel memristive Sprott A system (MSAS) through coupling a flux-controlled memristor with multi-piecewise linear memductance into the chaotic Sprott A system. From theoretical analysis and numerical simulations, the MSAS is shown to be able to generate any number of multi-type hidden attractors, including multi-one-scroll, multi-double-scroll and multi-double-wing hidden attractors. In addition, it has two kinds of multistabilities, that is, heterogeneous multistability and homogeneous multistability. Based on these unique properties, different numbers of coexisting heterogeneous hidden attractors and coexisting homogeneous hidden attractors are derived respectively by switching the memristor initial states. These interesting dynamical properties are comprehensively investigated using nonlinear analysis tools. Furthermore, hardware experiments are implemented to demonstrate the feasibility of the MSAS and the effectiveness of the MC method. Finally, a new pseudo-random number generator (PRNG) is proposed to explore the practical applications of the MSAS. Performance evaluation results verify the high-quality randomness of the designed PRNG.