In this paper, we report a novel memristor-based cellular neural network (CNN) without equilibrium points. Dynamical behaviors of the memristor-based CNN are investigated by simulation analysis. The results indicate that the system owns complicated nonlinear phenomena, such as hidden attractors, coexisting attractors, and initial boosting behaviors of position and amplitude. Furthermore, both heterogeneous multistability and homogenous multistability are found in the CNN. Finally, Multisim circuit simulations are performed to prove the chaotic characteristics and multistability of the system.

In this paper, we construct a quantum logistic-tent map and extend it to the fractional order. Using bifurcation portrait, Lyapunov exponent spectrum, and spectral entropy, its nonlinear characteristics are investigated. The analysis results illustrate that this fractional map possesses higher nonlinearity and is better suited for image encryption. Thus, the fractional quantum logistic-tent map as well as compressed sensing (CS) are utilized to create an image cryptosystem. The measurement matrix of CS is generated by this fractional map. Moreover, the map is also used for confusion and diffusion. In this encryption algorithm, the plaintext image is first sparsely represented with discrete wavelet transform (DWT). We then segment and reassemble the sparse image, and apply Arnold map to confuse the reassembled image. Next, a partial Hadamard matrix samples the image, and the pixel value is quantified with limited accuracy. Finally, the pixels of the image are diffused by two-way diffusion. This scheme integrates sparsity, block exchange, confusion, measurement acquisition, and diffusion. The simulation experiment finds that this image encryption approach possesses good security and compression performance.

This paper presents the construction of a 5D Euler equation using four sub-Euler equations with the coupling parameters and analyzes the conservation of Hamiltonian and Casimir energy. By breaking the conservation of Casimir energy, a 5D Hamiltonian conservative hyperchaotic system is developed. Phase diagrams, Lyapunov exponent spectra, and bifurcation diagrams are employed to investigate the nonlinear properties of the system. It is discovered that the system possesses dynamic characteristics such as amplitude control, multistability, transient quasi-period, and a wide constant range. The statistical properties of the pseudo-random sequences produced by the system are assessed via the National Institute of Standards and Technology (NIST). Lastly, the circuit simulation and STM32 platform are used to confirm the viability of the system.

Memtransistors, as multi-terminal devices with gate-tunable memristive behavior, offer new opportunities for nonlinear circuit design beyond conventional two-terminal memristors. The paper proposes a novel four-dimensional chaotic oscillator by integrating a three-terminal memtransistor model with a memristor. The mathematical models of both devices are established, and their equivalent circuits are presented. Based on the memtransistor model, a chaotic circuit is constructed, and its dynamical behavior is investigated by the Lyapunov exponent spectrum, bifurcation diagram, dynamical map, and other tools. It is found that the chaotic circuit has complex nonlinear characteristics and that the phenomenon of attractor coexistence exists. Furthermore, the chaotic system is discretized by the Euler approach, and experiments on an STM32-based circuit confirm the reliability of the theoretical analysis. This work provides a hardware-validated platform for studying memtransistor-based nonlinear circuits and may find applications in chaos-based secure communication and neuromorphic computing.