With the widespread application of audio communication in the internet of things, secure and efficient audio data transmission has become increasingly critical. However, existing chaos-based encryption schemes often face challenges in flexibly generating complex chaotic attractors and achieving a practical balance between security, flexibility, and efficiency. To address these limitations, this paper proposes a novel universal method for generating multi-structure chaotic attractors based on a quaternion rotation matrix transformation. This method enables flexible control over the position, scale, and number of wing units in attractors by configuring quaternion parameters and multi-level pulse function. Building upon this, we design a high-performance chaos-based audio encryption algorithm, and implement an encryption system for wireless transmission using a microcontroller and LoRa module. The system integrates audio recording, encryption, wireless transmission, and decryption. Comprehensive security analyses demonstrate the proposed algorithm achieves robust performance. The successful integration of flexible chaotic attractor design, robust cryptographic security, and hardware realization confirms the practical viability of our scheme for information transmission in resource-constrained environments.

The development of low-dimensional hyperchaotic maps with controllable dynamics and high randomness is both important and challenging. To address these issues, we propose a novel two-dimensional torus hyperchaotic map (2D-THM). This map is constructed through torus projections, which ensures global boundedness and produces diverse petal-like hyperchaotic attractors. Particularly, the torus parameters enable flexible control over attractor structure and pattern characteristics. Comparative analyses using numerical simulations and entropy metrics demonstrate that 2D-THM achieves superior complexity and robust hyperchaotic properties. Based on this map, a novel image encryption algorithm is presented. This algorithm utilizes attractor features to achieve high storage efficiency, making it particularly suitable for resource-constrained environments. Comprehensive security analyses confirm strong resistance to various attacks. Furthermore, this algorithm is implemented on FPGA platform, achieving an encryption time of 47 ms for a 1 MB image with low power consumption and efficient RAM usage, thereby validating its practical efficiency and hardware adaptability for real-world applications.

Designing a universal framework for configuring bionic spiking circuits is an attractive topic for spike-based applications. This paper comprehensively considers the electrophysiological properties of a biological neuron and electrical features of mem-elements, then presents a new universal framework for configuring fully mem-element-based bionic spiking circuits. The universal framework contains a current-controlled locally active memristor (LAM), a charge-controlled memcapacitor, and a flux-controlled meminductor to respectively characterize the electrophysiological properties of ion channels, liquid bilayer membrane, and electromagnetic induction of a biological membrane. The universal framework only involves the three mem-elements and a DC current stimulus. Afterward, a case of a mem-element emulator-based bionic spiking circuit is configured employing the universal framework. Numerical explorations and experimental measurements based on analog hardware circuits are performed to validate the effectiveness of the universal framework in generating abundant bifurcation behaviors and spiking activities. Actually, the universal framework is available for employing different mem-element emulators or physical mem-elements to construct bionic spiking circuits. The universal framework is extensible and sheds new light on the configuration of fully mem-element-based bionic spiking circuits.

An autonomous mobile robot with chaotic navigation, named chaotic mobile robot (CMR), has shown significant potential applications for dangerous or special duties in Internet of Things. As the control source of CMR, the application of novel chaotic dynamical systems with good design flexibility, topological transitivity, and sensitivity to initial conditions, will favor analyzing the whole workplace. To this purpose, a novel dual-route fractal process (DRFP) is proposed based on Julia and advanced Julia functions, which implements the automatic design of multifolded chaotic prototype models for given seed chaotic system. In comparison with the traditional Julia fractal process, the DRFP shows significant advantage in filling in the chaotic trajectory in empty inner space, which is beneficial to design CMR with high performance. The simulation and experiment are presented to validate the design feasibility of the DFRP. Finally, a two-wheeled differential drive system coupled with the chaotic model is designed to observe its navigation performances in either open region or bounded region with obstacles.

The generation of complicated grid hyperchaotic hidden attractors is an interesting but challenging work. Up to now, no grid hyperchaotic system with stable equilibria has been reported and implemented yet. This paper presents a two-step design scheme for constructing novel grid hyperchaotic system with only stable equilibria. First, the simple variable boosting is applied to a single-stable-equilibrium hyperchaotic system to generate offset boosted hyperchaotic hidden attractors in two directions. At this point, it is associated with the increase of the number of equilibria in corresponding directions. To solve this problem, the configuration of two specific sawtooth waveform functions implements the offset switching in two directions but only extends the number of the equilibria in a single direction. Meanwhile, all these equilibria have the same stability conditions that will not change with the increase of the grid. Consequently, various grid hyperchaotic hidden attractors are generated. Numerical simulations are presented to intuitively show the phase portraits and cross sections. Finally, hardware experiments using analog circuit implementation are presented to verify the feasibility of the grid hyperchaotic system.

As a classic paradigm of chaos generation, Chua’s circuit has been widely studied and applied in different fields. Various Chua’s circuits employing voltage-controlled Chua’s diodes have been designed and implemented, but rare such circuits employing current-controlled Chua’s diodes have been reported to date. Following the technical steps which Chua used to design the famous Chua’s circuit, this paper presents a systematic design procedure of the chaotic circuits employing current-controlled nonlinear resistors. Two simple circuit topologies are presented as paradigms, which respectively are dual to the classical Chua’s circuit and the canonical Chua’s circuit. In specific, we obtain two simple implementations of the dual Chua’s circuits consisting of two inductors, one capacitor, one passive/active linear resistor, and one piecewise-linear current-controlled Chua’s diode. The numerical simulations and the previously unreported physical implementations confirmed the feasibility of the design. Consequently, it enriches the genealogy of the Chua’s circuit family.

As a paradigm bridging the mathematical chaos to physical one, Chua’s circuit and its dimensionless Chua’s system have been widely studied and applied. From the completeness point of view, it is an interesting issue under investigation that how many potential Chua’s circuit variants exist within the framework of a single Chua’s system. Follow the duality principle in electrical circuits, this paper presents a Chua’s circuit employing ideal charge-controlled memristive model, which complements the circuit genealogy of the classical Chua’s system to four, i.e., Chua’s circuit, dual Chua’s circuit, memristive Chua’s circuit, and dual memristive Chua’s circuit (DMCC). To study the initial condition-related dynamical behaviors of the DMCC, we further present the flux-charge analysis. Some complex coexisting dynamics that cannot be typically observed in the voltage-current-domain have been investigated in the flux-charge-domain. Based on the dimensionless equations of the DMCC, an equivalent circuit is implemented for verification.

Bionic firing circuits are beneficial for bionic hardware applications. It is an attractive but challenging task to design a simple bionic firing circuit to generate spiking and bursting behaviors. To hit this aim, this paper newly proposes a universal configuration framework for mem-element-emulator-based bionic firing circuit, which deploys the charge-controlled memcapacitor and voltage-controlled locally active memristor (LAM) to characterize the electrophysiological behaviors of liquid bilayer and ion channels of a neuronal membrane, respectively. The configuration framework only contains one memcapacitor, LAM, DC voltage, and current stimulus. Then, a charge-controlled memcapacitor and an N-type LAM are employed as a case to verify the effectiveness of the configuration framework. Numerical simulations, PSpice circuit simulations, and discrete component-based hardware experiments are performed, which display that the bionic firing circuit can generate abundant spiking and bursting behaviors. One key feature is that the configuration framework can employ different charge-controlled memcapacitors and voltage-controlled LAMs to build more potential bionic firing circuits. To the authors’ knowledge, this configuration framework is extendable and sheds new light on the design of bionic firing circuits.

The systematic control of chaotic phase orbits in desired location and orientation favors of the generation of multiwing/scroll attractors for potential industrial applications, which is an attractive but challenging work. In this article, we present a universal matrix transformation method for generating multistructure chaotic attractors. First, several basic transformation matrices or their composite forms are chosen to implement multiplex control of a seed. On this foundation, applying it in a general 3-D system and further obtaining the universal transformed system. Taking the Lorenz system, Chua's system, and Rössler system as the seeds, we construct various multistructure attractors with custom-shaped distributions via stringing together multiple separate units. The novelties are that the method is universal, has wide applicability, and does not introduce any extra variables for state-extension. Numerical phase orbits and hardware implementations verified the feasibility of the method. A pseudorandom number generator with qualified performance is implemented to support its potential applications.

Analog circuit implementation of neuron model is an essential category of neuromorphic circuit since it can reproduce neuron firing patterns and assist in exploring neuron-based applications. The neuron models built by electrophysiological ion transport mechanism can effectively mimic the neuron firing patterns. However, they are rather difficult to implement on analog level because these neuron models involve complex exponential nonlinearities for characterizing the ion channels. Thanks to the superiorities of locally active memristor in constructing artificial neuron circuit, two locally active memristors are employed to characterize the sodium and potassium ion channels and then a memristive neuromorphic circuit is successfully built in this paper. Numerical simulations demonstrate that the memristive neuromorphic circuit can generate abundant firing patterns with respect to memristor- and stimulus-related parameters. Moreover, quasi-periodic bifurcation behavior and coexisting firing patterns are triggered by different memristor initial conditions. Employing off-the-shelf discrete circuit components, a PCB-based analog circuit is manually constructed and hardware experiments are executed. Experimental results captured from hardware measurements satisfactorily verify the numerically simulated ones and effectively show the feasibility of the memristive neuromorphic circuit in generating neuron firing patterns.

When chaotic sequences are used in engineering applications, their oscillating amplitudes need to be adjusted nondestructively. To accommodate this issue, this article presents a simple 2-D sine map. It can not only generate the chaotic sequences with high complexity, but also boost the oscillating amplitudes by switching their initial states. To show the complex dynamics of the sine map, this article investigates its control parameters-related dynamical behaviors and initials-boosted coexisting bifurcations using numerical methods. The results demonstrate that the oscillating amplitudes of chaotic sequences generated by the sine map can be nondestructively controlled by switching their initial states. This makes the sine map more suitable for many chaos-based engineering applications. Furthermore, we develop a microcontroller-hardware test platform to implement the sine map. The experimental results show that the platform synchronously outputs multichannel initials-controlled chaotic sequences. We also design a pseudorandom number generator to explore the application of the sine map.

Maximizing the lifetime is an important issue in the design of applications and protocols for wireless sensor networks (WSNs). Clustering sensor nodes is an effective topology control approach helping achieve this goal. In this paper, we present an energy efficiency protocol to prolong the network lifetime based on an improved particle swarm optimization (PSO) algorithm. The protocol takes both energy efficiency and transmission distance into consideration, and the relay nodes are used to balance the heavy consumption of cluster heads. In this way, the network results in better distributed sensors and a well-balanced clustering system enhancing the network's lifetime. We compare the proposed protocol with comparative protocols in different scenarios. Simulation results show that the proposed protocol performs well over other comparative protocols in various scenarios.