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.

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.

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.