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In this article, a periodic self-triggered impulsive (PSTI) control scheme is proposed to achieve synchronization of neural networks (NNs). Two kinds of impulsive gains with constant and random values are considered, and the corresponding synchronization criteria are obtained based on tools from impulsive control, event-driven control theory, and stability analysis. The designed triggering protocol is simpler, easier to implement, and more flexible compared with some previously reported algorithms as the protocol combines the advantages of the periodic sampling and event-driven control. In addition, the chaotic synchronization of NNs via the presented PSTI sampling is further applied to encrypt images. Several examples are also utilized to illustrate the validity of the presented synchronization algorithm of NNs based on PSTI control and its potential applications in image processing.

Cancer is recognized as one of the serious diseases threatening human health. Oncolytic therapy is a safe and effective new cancer treatment method. Considering the limited ability of uninfected tumor cells to infect and the age of infected tumor cells have a significant effect on oncolytic therapy, an age-structured model of oncolytic therapy involving Holling-Ⅱ functional response is proposed to investigate the theoretical significance of oncolytic therapy. First, the existence and uniqueness of the solution is obtained. Furthermore, the stability of the system is confirmed. Then, the local stability and global stability of infection-free homeostasis are studied. The uniform persistence and local stability of the infected state are studied. The global stability of the infected state is proved by constructing the Lyapunov function. Finally, the theoretical results are verified by numerical simulation. The results show that when the tumor cells are at the appropriate age, injection of the right amount of oncolytic virus can achieve the purpose of tumor treatment.

In ecosystems, almost all organisms suffer from external influences, which are assumed to be random perturbations. The aim of this paper is to investigate the effects of random perturbations on interacting populations. To solve this problem, we propose a discrete-time plant quality and larch budmoth interaction model with biological control. First of all, the model is theoretically analyzed, and the dynamic behavior of the population is qualitatively analyzed by numerical simulation. In addition, random perturbations are added to the model to observe the effects of random perturbations on the dynamic behavior of the budmoth population. The main results show that a random perturbation changes the number of blurred orbits of the system compared to the single population model with the same perturbation. Undeniably, it enhances the stability of the system. The model results, after adding random perturbations, are closer to reality, and in practice, we can also use random perturbations for resource management and pest control.

Pest control based on an economic threshold (ET) can effectively prevent excessive pest control measures such as pesticide abuse and overharvesting. The instinctive dispersal of pest populations in biological network patches for better survival poses challenges for pest management. As long as the pest density is controlled below the economic threshold and no pest outbreak occurs, the aim of pest management can be achieved and it is not necessary to completely remove the pests. This study focuses on the issues of chimera states and cluster solutions in regular bidirectional biological networks with state-dependent impulsive pest management. We consider the influence of two different control modes on the system states, namely global control and local control. Local control is found to be more likely to induce the chimera state. In addition, in the local coupling mode, a higher coupling strength is more likely to generate a coherent state, whereas a lower coupling strength is more likely to generate chimera and incoherent states. Furthermore, the cluster size is inversely related to the coupling strength under local coupling and global control.

All-dielectric nanostructures have attracted attention for highly efficient light manipulation. Higher Q-factor Fano resonance can be excited due to the rich phenomenology of optical modes supported by high-index dielectric materials with low intrinsic material loss, including both electric and magnetic multipolar Mie resonances. So far, there have been few studies done on the sensing with Fano-resonant all-dielectric resonator nanostructures. Here, an all-dielectric self-referenced optical sensor is numerically demonstrated based on Si quadrumers and mirror-symmetric 1-D photonic crystals (1DPCs) hybridstructure, operating at the infrared wavelength range with higher sensing performance and much more stable reference signal. Magnetic Fano resonance and Fabry-Perot resonance were combined into such a hybridstructure for the first time. The influences of the gap distance, including Δx and Δy , on the coupling effects between the Si nanodimers along the polarization direction and the 1DPCs are systematically discussed. The sensing performance has been numerically investigated in different analytes with the sensitivity and figure of merit (FOM) of 760 nm/RIU and 1515 RIU−1 respectively, which paves the way to be a much more sensitive detection of small refractive index changes in an unstable environment and suggests potential applications in biological and chemical sensing.

For nonsmooth Filippov systems, the stability of the system is assumed to be proved by nonsmooth Lyapunov functions, such as piecewise smooth Lyapunov functions. This extension was based on the Filippov solution and Clarke generalized gradient. However, it is difficult to estimate the gradient of a non-smooth Lyapunov function. In some cases, the nonsmooth system can be divided into continuous and discontinuous components. If the Lebesgue measure of the discontinuous components is zero, the smooth Lyapunov function can be utilized to prove the stability of the system owing to the inner product of the gradient of the Lyapunov function of the discontinuous components being zero. In this paper, we apply the smooth Lyapunov function to prove the stability of the nonsmooth ratio-dependent predator-prey system. In contrast to the existing literature, in this paper, although the system is divided into continuous and discontinuous components, the inner product of the gradient of the Lyapunov function of the discontinuous part is not zero but negative. In the proof of stability, the negative value condition is stricter than the zero-value condition. This proof method only needs to construct a smooth Lyapunov function, which is simpler than a non-smooth Lyapunov function or other methods.

By assuming a periodic variation in the intrinsic growth rate of the prey, a nonlinear ecological system with periodic forcing and state-dependent feedback control is proposed. The main purpose of the present paper is to study the dynamical behavior generated by periodic forcing and nonlinear impulse perturbations and their effects on pest control. To do this, we first investigate the existence and stability of the boundary periodic solution, and then we employ the numerical bifurcation techniques, mainly including one-dimensional and two-dimensional parameter bifurcation analyses, to reveal that the system exhibits rich and complex dynamic behaviors. Especially, period-adding bifurcation with chaos is found in the two-parameter bifurcation plane. Moreover, we find the periodic structure similar to Arnold tongues, and they are arranged according to the sequence of a Farey tree. In addition, one-dimensional bifurcation diagrams reveal the existence of order-[Formula: see text] periodic, and chaotic solutions, multiple coexisting attractors, period-doubling bifurcations, period-halving bifurcations, and so on. Finally, the effects of the initial population density of pests and natural enemies on the pulse frequency and the biological significance related to the numerical results are studied and discussed.

The neuronal state resetting model is a hybrid system, which combines neuronal system with state resetting process. As the membrane potential reaches a certain threshold, the membrane potential and recovery current are reset. Through the resetting process, the neuronal system can produce abundant new firing patterns. By integrating with the state resetting process, the neuronal system can generate irregular limit cycles (limit cycles with impulsive breakpoints), resulting in repetitive spiking or bursting with firing peaks which can not exceed a presetting threshold. Although some studies have discussed the state resetting process in neurons, it has not been addressed in neural networks so far. In this paper, we consider chimera states and cluster solutions in Hindmarsh-Rose neural networks with state resetting process. The network structures are based on regular ring structures and the connections among neurons are assumed to be bidirectional. Chimera and cluster states are two types of phenomena related to synchronization. For neural networks, the chimera state is a self-organization phenomenon in which some neuronal nodes are synchronous while the others are asynchronous. Cluster synchronization divides the system into several subgroups based on their synchronization characteristics, with neuronal nodes in each subgroup being synchronous. By improving previous chimera measures, we detect the spike inspire time instead of the state variable and calculate the time between two adjacent spikes. We then discuss the incoherence, chimera state, and coherence of the constructed neural networks using phase diagrams, time series diagrams, and probability density histograms. Besides, we further contrast the cluster solutions of the system under local and global coupling, respectively. The subordinate state resetting process enriches the firing mode of the proposed Hindmarsh-Rose neural networks.

A novel Filippov forest-pest system with threshold policy control (TPC) is established while an economic threshold (ET) is used to guide switching. The aim of our work is to address how to reasonably and successfully control pests by means of sliding dynamics for the Filippov system. On the basis of the above considerations, conditions for the existence and stability of equilibria of subsystems are addressed, and the sliding segments and several types of equilibria of the proposed system are defined. These equilibria include the regular/virtual equilibrium, pseudoequilibrium, boundary equilibrium, and tangent point. Further, not only are the relations between nullclines and equilibria of the Filippov system discussed, but the relations between pseudoequilibrium, nullclines, and the sliding segment are discussed. More importantly, four cases of sliding bifurcations of the Filippov system with respect to different types of equilibria of subsystems are investigated, and the corresponding biological implications concerning integrated pest management (IPM) are analyzed. Our results show that the points of intersection between nullclines are equilibria of the system, and the two endpoints of the sliding segment are on the nullclines. It is also verified that the pseudoequilibrium is the point of intersection of the sliding segment and nullclines of the Filippov system, and the pseudoequilibrium exists on the sliding segment. More interestingly, sliding dynamics analysis reveals that the Filippov system has sliding limit cycles, a bistable state and a stable refuge equilibrium point, and the optimal time and strategy for controlling pests are provided.

During the pest growth generations there exist a number of internal and external perturbations including birth pulses and pulse pesticide applications, which result in a complex growth pattern within each pest growth generation due to the variation of perturbation timings. In order to show how multiple pulse perturbations affect the dynamics of the pest population, we have extended the classical Fisher reaction-diffusion equation by involving instant birth and control perturbations. The main results indicate that the pulse perturbations have a remarkable influence on the existence and stability of a spatially homogeneous periodic solution. In particular, the birth rate and killing efficacy can affect the traveling wave and its spreading speed, while the timing of pesticide application does not make any effects on those threshold conditions. However, numerical investigations reveal that the timing of pesticide applications can significantly affect the spatial distributions of the pest population. Within each generation too early or too late pesticide application could result in a faster growth and wider spread of the pest, and the optimal timing of pesticide application is the middle of each generation provided that the efficacy of the pesticide is relatively low. Bifurcation analyses reveal that even generations and odd generations display a different spatial pattern, which depict some important issues related to the pest control and pest management, for example the different control strategies should be adopted for even and odd generations. To address how the spatial heterogeneity affects on the cost of the pest control, we further formulate the cost function to investigate the optimal pest control strategy, and the optimal spatial dependent killing rates which minimize the cost have been obtained numerically.

This paper investigates the impact of the threshold control strategy and environmental randomness on pest control. Firstly, a fixed-time impulsive stochastic ecosystem with IPM strategy is proposed, where the local and global existence of positive solution and the boundedness of expectation are discussed in detail. Moreover a sufficient condition for the extinction of the pest population with probability-1 is given. Then, a state-dependent stochastic ecosystem with IPM strategy is proposed. By employing the numerical simulations, the effects of ambient noise intensity on pest-outbreak are discussed. The result shows that there is a close relationship among the frequency of pest-outbreak, ET, the environmental perturbation intensity, and control measures. This study helps us to understand the impact of random factors on pest-outbreak frequency by theoretical derivations and numerical simulations; the results have directive significance in the design of an optimal control strategy for the department of ecological agriculture.

Compared to the reported 5 × 5 spot arrays, we propose a way of generating a 5 × 5 spot array with much higher efficiency and better uniformity by using two crossed single-groove gratings. Normally...

A novel periodically forced Filippov Holling II prey-predator model by applying threshold policy control (TPC) and integrated pest management (IPM) strategies is proposed, and the periodic forcing is described as a Fourier series with different forcing terms. Our work is aim to address how periodic forcing affects dynamic behaviors of the proposed system and to reasonably realize pest control. Based on the above considerations, the relations between sliding region and sliding periodic solution of the Filippov system are analyzed. Then, the existence conditions of sliding periodic solution and its global stability are addressed. Further, numerical investigations related to bifurcation analysis of crucial parameters including the amplitude of forcing terms, economic threshold (ET) and the frequency of forcing terms are discussed. More importantly, the real biological implications are also addressed. Our results show that the globally stable sliding periodic solution could always lie in the sliding region, which indicates that the density of pest populations cannot reach and exceed the economic injury level (EIL), namely, the pest control is successful. Moreover, the results reveal that various complex dynamics of the Filippov system contains multiple attractors coexistence, switching transients and chaotic phenomena. In addition, the attraction basins of the coexisting attractors reveal that these two populations could be monitored and tracked carefully for the successful pest control, which depends on their initial density.

There are many challenges to coupling the macroscale to the microscale in temporal or spatial contexts. In order to examine effects of an individual movement and spatial control measures on a disease outbreak, we developed a multiscale model and extended the semi-stochastic simulation method by linking individual movements to pathogen’s diffusion, linking the slow dynamics for disease transmission at the population level to the fast dynamics for pathogen shedding/excretion at the individual level. Numerical simulations indicate that during a disease outbreak individuals with the same infection status show the property of clustering and, in particular, individuals’ rapid movements lead to an increase in the average reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}R0, the final size and the peak value of the outbreak. It is interesting that a high level of aggregation the individuals’ movement results in low new infections and a small final size of the infected population. Further, we obtained that either high diffusion rate of the pathogen or frequent environmental clearance lead to a decline in the total number of infected individuals, indicating the need for control measures such as improving air circulation or environmental hygiene. We found that the level of spatial heterogeneity when implementing control greatly affects the control efficacy, and in particular, an uniform isolation strategy leads to low a final size and small peak, compared with local measures, indicating that a large-scale isolation strategy with frequent clearance of the environment is beneficial for disease control.

Integrodifference equations have been widely used to describe the spatiotemporal dynamics of a population. Here, we first extended the discrete Beverton–Holt model, to model the effects of an instantaneous control measure within each generation on a population’s growth. Then we investigated the effects of instantaneous killing rate and timing of pesticide application on a pest’s dynamics, together with the effects of a spatial factor on the existence of a travelling wave solution, its spreading speed and asymptotic stability, and the occurrence of paradoxical effects. The main results indicate that the instantaneous killing rate significantly influences the existence of a travelling wave and its speed of spread, while the timing of pesticide applications does not. In order to address how such dynamic complexities affect the above results, we included an interruption constant into the model which can generate chaotic dynamics. The results indicate that the pesticide efficacy not only affects the existence of a travelling wave and its speed of spread, but it can also produce paradoxical effects, i.e. low pesticide efficacy can result in an increase, not a decrease, of the stable population size, while high pesticide efficacy could inhibit the pests growth. Furthermore, different patterns of stable population sizes between odd and even generations can be produced. The results reveal that the pest control tactics should be designed according to the spatial characteristics and the pest generation.

We present a type of generalized circular Dammann gratings (GCDGs) with controllable impulse ring profiles. Different from impulse rings generated by traditional circular Dammann gratings, the intensity profile of impulse rings can be tuned by redesigning the phase structure of GCDGs. Also, the physical picture behind this controllable impulse ring profile is given clearly. As examples, four one-order binary (0, $\pi $ ) GCDGs are designed and fabricated for generation of impulse rings with four different intensity profiles. In addition, GCDGs with continuous-phase profile are also demonstrated for generation of multiple concentric equal-intensity impulse rings with different intensity profiles. This type of impulse rings with tunable intensity profiles will enrich the function of CDGs, and it should be of high interest for its potential applications in various realms, such as structured pumping laser, novel optical manipulation, generation of dark perfect vortices, and optical testing and measurement.

In this paper, we propose a nonconvex and nonsmooth total generalized variation (TGV) model for image restoration, which can provide an even sparser representation of the variation of the image function than the traditional TGV model that uses convex l 1 norm to measure the variation. New model combines the advantages of nonconvex regularization and TGV regularization, and can preserve image edges well and simultaneously alleviate the staircase effects often arising in the total variation based models. Two different iteratively reweighed algorithms are introduced to numerically solve the proposed nonconvex and nonsmooth TGV model. Numerical results show that the proposed model is effective in edge-preserving and staircase-reduction in image restoration. In addition, compared with several state-of-the-art variational models, the proposed model has the best performance in terms of PSNR and MSSIM values.

To solve the dynamic problem of different activities in human activity recognition research, an activity recognition method based on a multiplex limited penetrable visibility graph is proposed. The 21 pressure values for each sampling are mapped to nodes in the first-layer network; then the average path length of nodes in the asynchronous periodic network is obtained, and the second-layer network used to explore different activities is built. Finally, the characteristic parameters and dynamic characteristics of different activities are explored and analyzed. The experimental results demonstrate that through the joint distribution of the average clustering coefficient and the maximum degree parameter of the node, the discrimination problems of different postures can be better realized, and it has good adaptability. It provides a new approach to gait recognition research that can be used in medical clinical diagnosis, rehabilitation training, and public health.

Better performances of two-dimensional (2D) grating are required recently, such as polarization independence, high efficiency, wide bandwidth and so forth. In this paper, we propose a 2×2 2D silver cylindrical array grating with excellent polarization-independent high diffraction efficiency (DE) over communication band for beam splitting. The grating was calculated by rigorous coupled wave analysis (RCWA) and can achieve over 24% DE of four first diffraction orders at 1550 nm with nonuniformity of 1.43% in both transverse electric (TE) and transverse magnetic (TM) polarizations, which is a significant improvement over previous reports. The holographic exposure technology, wet chemical development process and electron beam evaporation were used to fabricate the 2D grating. The correctness and accuracy of the calculation are fully verified with the measurement result of fabricated grating. Excellent performances of the 2D splitter we proposed will have great potential for applications in optical communication, semiconductor manufacturing and displacement measurement.