This article investigates cluster synchronization (CS) of individuals during an epidemic using a coupled nonlinear network that integrates diffusion-coupled nonlinear systems with an susceptible-infected-recovered (SIR) virus model. To better reflect real-life scenarios, individuals are grouped into clusters, and the model incorporates recovery rates that vary according to collective behavior patterns. The study focuses on analyzing the relationship between CS behavior and the progression of virus transmission within the network. By ensuring that the directed graph satisfies the cluster input equivalence condition and that the system’s Jacobian matrix remains bounded, contraction analysis is employed to establish conditions for achieving CS, which are influenced by the virus’s state. Furthermore, the impact of CS on epidemic dynamics is explored. Numerical simulations validate the theoretical findings.

A functional neuron has been developed from a simple neural circuit by incorporating a phototube and a thermistor in different branch circuits. The physical field energy is controlled by the photocurrent across the phototube and the channel current across the thermistor. The firing mode of this neuron is controlled synchronously by external temperature and illumination. There is energy diversity when two functional neurons are exposed to different illumination and temperature conditions. As a result, synapse connections can be created and activated in an adaptive way when field energy is exchanged between neurons. We propose two kinds of criteria to discuss the enhancement of synapse connections to neurons. The energy diversity between neurons determines the increase of the coupling intensity and synaptic current for neurons, and the realization of synchronization is helpful in maintaining energy balance between neurons. The first criterion is similar to the saturation gain scheme in that the coupling intensity is increased with a constant step within a certain period until it reaches energy balance or complete synchronization. The second criterion is that the coupling intensity increases exponentially before reaching energy balance. When two neurons become non-identical, phase synchronization can be controlled during the activation of synapse connections to neurons. For two identical neurons, the second criterion for taming synaptic intensity is effective for reaching complete synchronization and energy balance, even in the presence of noise. This indicates that a synapse connection may prefer to enhance its coupling intensity exponentially. These results are helpful in discovering why synapses are awaken and synaptic current becomes time-varying when any neurons are excited by external stimuli. The potential biophysical mechanism is that energy balance is broken and then synapse connections are activated to maintain an adaptive energy balance between the neurons. These results provide guidance for designing and training intelligent neural networks by taming the coupling channels with gradient energy distribution.

The magnetic induction effects have been emulated by various continuous memristive models but they have not been successfully described by a discrete memristive model yet. To address this issue, this article first constructs a discrete memristor and then presents a discrete memristive Rulkov (m-Rulkov) neuron model. The bifurcation routes of the m-Rulkov model are declared by detecting the eigenvalue loci. Using numerical measures, we investigate the complex dynamics shown in the m-Rulkov model, including regime transition behaviors, transient chaotic bursting regimes, and hyperchaotic firing behaviors, all of which are closely relied on the memristor parameter. Consequently, the involvement of memristor can be used to simulate the magnetic induction effects in such a discrete neuron model. Besides, we elaborate a hardware platform for implementing the m-Rulkov model and acquire diverse spiking-bursting sequences. These results show that the presented model is viable to better characterize the actual firing activities in biological neurons than the Rulkov model when biophysical memory effect is supplied.

The digital image, as the critical component of information transmission and storage, has been widely used in the fields of big data, cloud and frog computing, Internet of things, and so on. Due to large amounts of private information in the digital image, the image protection is fairly essential, and the designing of the encryption image scheme has become a hot issue in recent years. In this paper, to resolve the shortcoming that the probability density distribution (PDD) of the chaotic sequences generated in the original two-dimensional coupled map lattice (2D CML) model is uneven, we firstly proposed an improved 2D CML model according to adding the offsets for each node after every iteration of the original model, which possesses much better chaotic performance than the original one, and also its chaotic sequences become uniform. Based on the improved 2D CML model, we designed a compressive image encryption scheme. Under the condition of different keys, the uniform chaotic sequences generated by the improved 2D CML model are utilized for compressing, confusing, and diffusing, respectively. Meanwhile, the message authentication code (MAC) is employed for guaranteeing that the encryption image be integration. Finally, theoretical analysis and simulation tests both demonstrate that the proposed image encryption scheme owns outstanding statistical, well encryption performance, and high security. It has great potential for ensuring the digital image security in application.

Biological neurons can receive inputs and capture a variety of external stimuli, which can be encoded and transmitted as different electric signals. Thus, the membrane potential is adjusted to activate the appropriate firing modes. Indeed, reliable neuron models should take intrinsic biophysical effects and functional encoding into consideration. One fascinating and important question is the physical mechanism for the transcription of external signals. External signals can be transmitted as a transmembrane current or a signal voltage for generating action potentials. We present a photosensitive neuron model to estimate the nonlinear encoding and responses of neurons driven by external optical signals. In the model, a photocell (phototube) is used to activate a simple FitzHugh-Nagumo (FHN) neuron, and then external optical signals (illumination) are imposed to excite the photocell for generating a time-varying current/voltage source. The photocell-coupled FHN neuron can therefore capture and encode external optical signals, similar to artificial eyes. We also present detailed bifurcation analysis for estimating the mode transition and firing pattern selection of neuronal electrical activities. The sampled time series can reproduce the main characteristics of biological neurons (quiescent, spiking, bursting, and even chaotic behaviors) by activating the photocell in the neural circuit. These results could be helpful in giving possible guidance for studying neurodynamics and applying neural circuits to detect optical signals.

Nonlinear oscillators and circuits can be coupled to reach synchronization and consensus. The occurrence of complete synchronization means that all oscillators can maintain the same amplitude and phase, and it is often detected between identical oscillators. However, phase synchronization means that the coupled oscillators just keep pace in oscillation even though the amplitude of each node could be different. For dimensionless dynamical systems and oscillators, the synchronization approach depends a great deal on the selection of coupling variable and type. For nonlinear circuits, a resistor is often used to bridge the connection between two or more circuits, so voltage coupling can be activated to generate feedback on the coupled circuits. In this paper, capacitor coupling is applied between two Pikovsk-Rabinovich (PR) circuits, and electric field coupling explains the potential mechanism for differential coupling. Then symmetric coupling and cross coupling are activated to detect synchronization stability, separately. It is found that resistor-based voltage coupling via a single variable can stabilize the synchronization, and the energy flow of the controller is decreased when synchronization is realized. Furthermore, by applying appropriate intensity for the coupling capacitor, synchronization is also reached and the energy flow across the coupling capacitor is helpful in regulating the dynamical behaviors of coupled circuits, which are supported by a continuous energy exchange between capacitors and the inductor. It is also confirmed that the realization of synchronization is dependent on the selection of a coupling channel. The approach and stability of complete synchronization depend on symmetric coupling, which is activated between the same variables. Cross coupling between different variables just triggers phase synchronization. The capacitor coupling can avoid energy consumption for the case with resistor coupling, and it can also enhance the energy exchange between two coupled circuits.