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%.

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.

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.

Discrete memristors have been employed in discrete maps for the purpose of chaos generation and regulation. In this paper, a novel universal model for discrete memristors is proposed to generate multi-attractors. The classical Hénon map and Rulkov neuron are chosen as two examples to verify the effectiveness of the proposed memristor. Coexisting homogeneous attractors are identified in the phase space by memristor-induced offset boosting. An arbitrarily desired number of coexisting attractors is extracted by the appropriate feedback strength of the memristor. What adds further interest to this case is that the amplitude is rescaled by a memristor-related parameter that works well over an infinite range. Number-related parameters are extracted to rescale the oscillation range of the chaotic signals. Moreover, CH32-based circuit implementation is built, which aligns with numerical simulation results. Finally, coexisting homogeneous chaotic signals are tested to explore their robust performance in the application of pseudo-random number generator.