In this brief a simple three-dimensional sine chaotic system formed by six terms is presented. The only one nonlinear term, i.e., the sinusoidal function makes the system have infinitely many equilibria. This prominent feature lead to infinitely many coexisting self-excited and hidden attractors with the same or different shapes, also namely homogenous multistability or heterogenous multistability. Furthermore, the multiple equilibria make the system successfully generate multi-scroll attractors. These complicated dynamical behaviors are numerically studied and further experimentally demonstrated by microcontroller-based hardware platform.

Base on different biological neuronal systems, various memristive neuron and neuron network models are generated. In this paper, a three-neurons-based Hopfield neural network with two biological neural mechanisms is investigated, with one of three neurons exposed to electromagnetic radiation and one of the synaptic weights replaced by a memristor. The effects of electromagnetic radiation and memristive synaptic weight on neural networks are investigated. It is found that coexisting behaviors exist in the neural network by adjusting the memristive synaptic weight. Moreover, infinitely many coexisting behaviors are observed by changing the initial electromagnetic radiation. That is, both of them are critical to the system and have the potential to complicate it. Furthermore, circuits of the neural network are implemented in Pspice and DSP board, and the experimental results are in agreement with numerical ones.

In this paper, a new sinusoidal cascade chaotic map model is proposed, which constructs chaotic system by sinusoidal cascade of two identical 1D chaotic maps. This model can generate 1D chaotic system with wider parameter range and wider chaotic region. To verify its application in image encryption, a chaotic image encryption algorithm based on spiral traversal and finite field bidirectional diffusion is proposed. The pseudo-random sequences generated by three kinds of 1D chaotic maps improved by the sinusoidal cascade chaotic map model are used as the ciphers of the cryptosystem. Among them, SHA-256, SHA-512 and plain image are combined to generate the initial value of the system. The experimental results and security analysis show that the encryption algorithm designed in this paper can effectively resist exhaustive attack, differential attack, noise attack and so on, and the proposed model has superior performance in encryption speed and security.

Compressed sensing (CS) theory has attracted widespread attention in recent years and has been widely used in signal and image processing, such as underdetermined blind source separation (UBSS), magnetic resonance imaging (MRI), etc. As the main link of CS, the goal of sparse signal reconstruction is how to recover accurately and effectively the original signal from an underdetermined linear system of equations (ULSE). For this problem, we propose a new algorithm called the weighted regularized smoothed $L_0$ -norm minimization algorithm (WReSL0). Under the framework of this algorithm, we have done three things: (1) proposed a new smoothed function called the compound inverse proportional function (CIPF); (2) proposed a new weighted function; and (3) a new regularization form is derived and constructed. In this algorithm, the weighted function and the new smoothed function are combined as the sparsity-promoting object, and a new regularization form is derived and constructed to enhance de-noising performance. Performance simulation experiments on both the real signal and real images show that the proposed WReSL0 algorithm outperforms other popular approaches, such as SL0, BPDN, NSL0, and L ${}_p$ -RLSand achieves better performances when it is used for UBSS.

This paper proposes a chaotic color image encryption scheme based on DNA-coding calculations and arithmetic over the Galois field. Firstly, three modified one-dimensional (1D) chaotic maps with larger key space and better chaotic characteristics are presented. The experimental results show that their chaotic intervals are not only expanded to 0,15, but their average largest Lyapunov Exponent reaches 10. They are utilized as initial keys. Secondly, DNA coding and calculations are applied in order to add more permutation of the cryptosystem. Ultimately, the numeration over the Galois field ensures the effect for the diffusion of pixels. The simulation analysis shows that the encryption scheme proposed in this paper has good encryption effect, and the numerical results verify that it has higher security than some of the latest cryptosystems.