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 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.