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This paper examines the dynamic behavior of a particular category of discrete predator-prey system that feature both fear effect and refuge, using both analytical and numerical methods. The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are computed using the center manifold theorem and bifurcation theory. Additionally, numerical simulations are employed to illustrate the bifurcation phenomenon and chaos characteristics. The results demonstrate that period-doubling and Hopf bifurcations are two typical routes to generate chaos, as evidenced by the calculation of the maximum Lyapunov exponents near the critical bifurcation points. Finally, a feedback control method is suggested, utilizing feedback of system states and perturbation of feedback parameters, to efficiently manage the bifurcations and chaotic attractors of the discrete predator-prey model. [ABSTRACT FROM AUTHOR]

In this paper, the limit cycles and local bifurcation of critical periods for a class of switching Z 2 equivariant quartic system with two symmetric singularities are investigated. First, through the computation of Lyapunov constants, the conditions of the two singularities to become the centers are determined. Then, we prove that there are at most 18 limit cycles with a distribution pattern of 9-9 around the two symmetric singular points of the system. Numerical simulation is conducted to validate the obtained results. Furthermore, by calculating the period constants, we determine the conditions for the critical point to be a weak center of finite order. Finally, the number of local critical periods that bifurcate from the equilibrium point under the center conditions is discussed. This study presents the first example of a quartic switching smooth system with 18 limit cycles and 4 local critical periods bifurcating from two symmetric singular points. [ABSTRACT FROM AUTHOR]

This paper presents synchronization of mixed continuous-discrete complex network via impulse-quantizing approach. A delay-partitioning group strategy is proposed and impulse-quantizing control is designed to derive theoretical criteria ensuring scale-type synchronization of complex networks. Our results show that synchronization of mixed continuous-discrete complex networks can be realized by controlling delay-partitioning subgroup nodes with impulsive quantization. The theoretical results give scale-limited sufficient conditions for quantized synchronization relying on control gains, impulsive intervals, and delays. A numerical simulation is given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents the dispersal effect on a prey-predator model with three-patch states incorporating a strong Allee effect on the first two prey populations. The prey species are considered to be mutable to exhibit a balanced dispersal between the patches. The dispersal among patches is directed through lower fit patches to higher fit patches. This paper derives a new approach for dispersal and Allee's effect with the specific condition on the stability on a three-patch of a three-species prey-predator anticipated system. The persistence of the system is observed because of the dispersal effect on the three-patch prey-predator system. The numerical simulations of analytical findings are presented using hypothetical parameter values to relate real-world prey-predator situations for balancing ecology. [ABSTRACT FROM AUTHOR]

The application and economic efficiency evaluation mode of traditional composition in the field of modern music cannot meet the needs of various types of music in China, especially Guqin music. Based on this, this paper studies the big data simulation model of Guqin sound synthesis and plucking based on computer composition technology. The computer composition technology uses the discrete dynamic modeling technology of complex system to complete the computer simulation of Guqin sound through the analysis of the correlation between Guqin music data and realizes the storage and analysis of the generated Guqin sound data. In addition, the technology can analyze the data information of composition mode in the piano sound plucking simulation model with the classical Guqin music data stored in the cloud system over the years and then feed it back to relevant professionals for verification. The experimental results show that the Guqin sound simulation model can efficiently compare and analyze the melody and other data of classical Guqin sound with the simulated Guqin sound and can realize secondary data mining. This paper studies the application of computer composition method based on discrete dynamic modeling technology in Guqin sound simulation, which has certain reference significance for improving the cloud data in China's modern music field and the intelligent construction of Guqin sound data cloud storage system. [ABSTRACT FROM AUTHOR]

In this paper, we consider a general time-space discrete host-parasitoid model with the periodic boundary conditions. We analyzed and obtained some usual conditions, such as Turing instability occurrence, Flip bifurcation occurrence, and Neimark-Sacker bifurcation occurrence. We also find several multiple bifurcation phenomena, such as 1 : 2 Resonance, Neimark-Sacker-Flip bifurcation, Neimark-Sacker-Neimark-Sacker bifurcation, Neimark-Sacker-Flip-Flip bifurcation, induced by diffusion. In a modified Nicholson-Bailey model, employing the mutual interference and diffusive interaction as bifurcation parameters, there appear route from standing Turing instability to multiple bifurcations by changing diffusive parameters. Some numerical simulations of the modified Nicholson-Bailey model support these corollaries. [ABSTRACT FROM AUTHOR]

This paper studies Lyapunov stability at a point and its application in the Cournot duopoly game. We first explore the relationship between Lyapunov stability at a point, nonsensitivity and non-Devaney chaos and find that a dynamical system is nonsensitive and non-Devaney chaotic if there is a point in this system such that it is Lyapunov stable at that point. We next prove a group of equivalent characterizations of Lyapunov stability at a point to deduce the composite theorems and product theorems of Lyapunov stability at a point, and then we prove three equivalent characterizations of the Cournot duopoly system to demonstrate that this system is Lyapunov stable at its unique nonzero fixed point (Cournot equilibrium point) when the unit costs of the Cournot double oligarchies satisfy certain conditions. Therefore, we conclude that the Cournot duopoly system is safe relative to both sensitivity and Devaney chaos. The robustness of our results are also verified by conducting numerical simulations in the Cournot duopoly game. [ABSTRACT FROM AUTHOR]

This paper analyzes the development prospects of zinc-nickel battery industry, further investigates the industry competition in existing markets by mathematical modeling, calculates the equilibrium price and profit of the oligarch competition by using the method of Stackelberg equilibrium and Nash equilibrium, and makes a comparison between them. Then, we study and model the case of renting and selling simultaneously. In addition, we also study the impact of futures prices on the zinc-nickel battery companies and carry out numerical simulation. At the end of this paper, we analyze the location of zinc-nickel battery enterprises and the industry development under the COVID-19 pandemic. The finding show that the reduction of raw material cost is of great help to the development of the zinc-nickel battery industry. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to study the formation of singularity for a coupled system of wave equations with damping terms, negative mass terms, and divergence form nonlinearities. Upper bound lifespan estimates of solutions to the system are obtained by using the iteration method. The results are the same as the corresponding coupled system of the wave equation with power nonlinearities v p and u q . To the best of our knowledge, the results in Theorems 1–5 are new. In addition, the variation trend of the wave is analyzed by using numerical simulation. [ABSTRACT FROM AUTHOR]

Electronic power converters are in a state of exhibiting some complex features which can be influenced by the converter's structure parameters and load, as well as its pulse period. In this paper, we propose to investigate these phenomena occurring in the dc/dc buck converter by carrying out the dynamics of the said system when it exhibits the fingerprints of frequency-dependent pinched hysteresis loops. The essential part of this study is consecrated to the nonlinear dynamics when the converter load is memristive. Under two kinds of switch states, the independent nonlinear models and equations are derived which provide a complete dynamics description of the system under investigation. The dynamics analysis is performed by making use of bifurcation tools, phase portraits, and two parameters Lyapunov diagrams showing that the system depicts very rich and striking behaviors such as periodic orbits, period-doubling bifurcation, quasiperiodicity, chaos, and pinched hysteresis loops of the memristive load. Finally, the numerical simulation results are in almost perfect agreement with the analog result obtained with PSIM. The results obtained in this work have not yet been reported in the literature to the best of our knowledge and thus deserve dissemination. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamic behavior of a stochastic tungiasis model for public health education. First, the existence and uniqueness of global positive solution of stochastic models are proved. Secondly, by constructing Lyapunov function and using It o ^ formula, sufficient conditions for disease extinction and persistence in the stochastic model are proved. Thirdly, under the condition of disease persistence, the existence and uniqueness of an ergodic stationary distribution of the model is obtained. Finally, the importance of public health education in preventing the spread of tungiasis is illustrated through the combination of theoretical results and numerical simulation. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time synchronization of complex dynamical networks with nondelayed and delayed coupling. By designing a simple continuous function controller, sufficient criteria for finite-time synchronization of dynamical networks with nondelayed and delayed coupling are obtained. As a special case, the continuous function controller designed in this paper may be the simplest and easy to implement for the finite-time synchronization of dynamical networks without delay. Finally, numerical simulations are given to verify the effectiveness of the conclusions presented in this paper. [ABSTRACT FROM AUTHOR]

The synchronization of states is important to sustain the energy of consumers at any given time for power networks. This paper focuses on the multi-area power network model and then analyzes the cluster synchronization of this kind of network comprised of a third-order chaotic power system. Specifically, we investigate the rich dynamic properties of the single third-order power system. Furthermore, the multi-area network model with the chaotic power system is proposed and the adaptive controller is designed to achieve cluster synchronization. Combining analytical considerations with numerical simulations on a small-scale network, we address the cluster synchronous performance in the multi-area power network. Therefore, our results can provide a basic physical picture for power system dynamics and enable us to further understand the complex dynamical behavior in the multi-area power network. [ABSTRACT FROM AUTHOR]

The realization of breakthrough innovation with high risk and uncertainty has always been the focus of the theory and practice of technological innovation. Based on the supernetwork theory, this paper constructs a supernetwork equilibrium model about deep convergence of enterprise alliance for breakthrough innovation and uses numerical simulation tools to find out the equilibrium conditions for deep convergence of enterprise alliance in different stages of breakthrough innovation. It is not only conducive to understand the process of enterprise alliance's deep convergence in "Creativity-Research-Production-Sales" but also helpful to understand the roles that deep convergence in enterprise alliance can play in achieving breakthrough innovation. It not only expands the existing research on breakthrough innovation but also provides a scientific reference for the deep convergence of enterprise alliance in practice. [ABSTRACT FROM AUTHOR]

In this paper, we study a Leslie–Gower predator-prey model with harvesting effects. We carry out local bifurcation analysis and stability analysis. Under certain conditions, the model is shown to undergo a supercritical Hopf bifurcation resulting in a stable limit cycle. Numerical simulations are presented to illustrate our theoretic results. [ABSTRACT FROM AUTHOR]

In recent years, with the rapid development of the Internet and the Internet of Things, network security is urgently needed. Malware becomes a major threat to network security. Thus, the study on malware propagation model plays an important role in network security. In the past few decades, numerous researchers put up various kinds of malware propagation models to analyze the dynamic interaction. However, many works are only concerned with the integer-order malware propagation models, while the investigation on fractional-order ones is very few. In this paper, based on the earlier works, we will put up a new fractional-order delayed malware propagation model. Letting the delay be bifurcation parameter and analyzing the corresponding characteristic equations of considered system, we will establish a set of new sufficient conditions to guarantee the stability and the existence of Hopf bifurcation of fractional-order delayed malware propagation model. The study shows that the delay and the fractional order have important effect on the stability and Hopf bifurcation of considered system. To check the correctness of theoretical analyses, we carry out some computer simulations. At last, a simple conclusion is drawn. The derived results of this paper are completely innovative and play an important guiding role in network security. [ABSTRACT FROM AUTHOR]

This paper deals with the dynamical behaviors for a computer viruses model with age structure, where the loss of the acquired immunity and delay are incorporated. Through some rigorous analyses, an explicit formula for the basic reproduction number of the model is calculated, and some results about stability and instability of equilibria for the model are established. These findings show that the age structure and delay can produce Hopf bifurcation for the computer viruses model. The numerical examples are executed to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic competitive model with distributed time delays and Lévy jumps is formulated. With or without a polluted environment, the model is denoted by (M) or (M0), respectively. The existence of positive solution, persistence in mean, and extinction of species for (M) and (M0) are both studied. The sufficient criteria of stability in distribution for model (M) is obtained. Finally, some numerical simulations are given to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, complex dynamical behaviors of a predator-prey system with the Beddington–DeAngelis functional response and the Allee-like effect on predator were studied by qualitative analysis and numerical simulations. Theoretical derivations have given some sufficient and threshold conditions to guarantee the occurrence of transcritical, saddle-node, pitchfork, and nondegenerate Hopf bifurcations. Computer simulations have verified the feasibility and effectiveness of the theoretical results. In short, we hope that these works could provide a theoretical basis for future research of complexity in more predator-prey ecosystems. [ABSTRACT FROM AUTHOR]

Information spreading dynamics on the temporal network is a hot topic in the field of network science. In this paper, we propose an information spreading model on an activity-driven temporal network, in which a node is accepting the information dependents on the cumulatively received pieces of information in its recent two steps. With a generalized Markovian approach, we analyzed the information spreading size, and revealed that network temporality might suppress or promote the information spreading, which is determined by the information transmission probability. Besides, the system exists a critical mass, below which the information cannot globally outbreak, and above which the information outbreak size does not change with the initial seed size. Our theory can qualitatively well predict the numerical simulations. [ABSTRACT FROM AUTHOR]

The collaborative development of complex products has gradually developed into a "main manufacturer-suppliers" mode, under which the manufacturing enterprises form a complex product collaborative manufacturing supply chain network. Quality risks which bring enormous hidden danger to the product quality can be propagated and accumulate along the supply chain. It is of great significance to quantify the propagation mechanism of quality risk between supply chain network nodes and identify the key quality risk factor that causes fluctuation of product quality. This study for the first time applies the SoV into the research on quality risk propagation of complex product collaborative manufacturing supply chain network. Firstly, this paper uses the CN to construct a complex product collaborative manufacturing supply chain network according to its characteristics. Secondly, on the basis of SoV, the quality risk propagation model is established. Thirdly, we put forward a method to identify the key quality risk factors of supply chain network based on the risk propagation effect. Lastly, a numerical simulation is given to verify the effectiveness of the model and its identification method. The results reveal that the quality risk propagation includes the vertical propagation within enterprises and the horizontal propagation from the lower-level enterprises to the upper-level enterprises of the supply chain. The quality risks of an enterprise are determined by its own quality risk factors and the quality risk passed by the lower-level enterprises. [ABSTRACT FROM AUTHOR]

The collaborative development of complex products has gradually developed into a "main manufacturer-suppliers" mode, under which the manufacturing enterprises form a complex product collaborative manufacturing supply chain network. Quality risks which bring enormous hidden danger to the product quality can be propagated and accumulate along the supply chain. It is of great significance to quantify the propagation mechanism of quality risk between supply chain network nodes and identify the key quality risk factor that causes fluctuation of product quality. This study for the first time applies the SoV into the research on quality risk propagation of complex product collaborative manufacturing supply chain network. Firstly, this paper uses the CN to construct a complex product collaborative manufacturing supply chain network according to its characteristics. Secondly, on the basis of SoV, the quality risk propagation model is established. Thirdly, we put forward a method to identify the key quality risk factors of supply chain network based on the risk propagation effect. Lastly, a numerical simulation is given to verify the effectiveness of the model and its identification method. The results reveal that the quality risk propagation includes the vertical propagation within enterprises and the horizontal propagation from the lower-level enterprises to the upper-level enterprises of the supply chain. The quality risks of an enterprise are determined by its own quality risk factors and the quality risk passed by the lower-level enterprises. [ABSTRACT FROM AUTHOR]

Based on the feature of projection operator under box constraint, by using convex analysis method, this paper proposed three robust linear systems to solve a class of quadratic optimization problems. Utilizing linear matrix inequality (LMI) technique, eigenvalue perturbation theory, Lyapunov-Razumikhin method, and LaSalle’s invariance principle, some stable criteria for the related models are also established. Compared with previous criteria derived in the literature cited herein, the stable criteria established in this paper are less conservative and more practicable. Finally, a numerical simulation example and an application example in compressed sensing problem are also given to illustrate the validity of the criteria established in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new restricted Liu estimator in a partially linear model when addition linear constraints are assumed to hold. We also consider the asymptotic normality of the new estimator. Finally, a numerical example and a simulation study are listed to illustrate the performance of the new estimator. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in finding the periodic oscillation of seasonally forced SEIR models with pulse vaccination. Many infectious diseases show seasonal patterns of incidence. Pulse vaccination strategy is an effective tool to control the spread of these infectious diseases. Assuming that the seasonally dependent transmission rate is a T-periodic forcing, we obtain the existence of positive T-periodic solutions of seasonally forced SEIR models with pulse vaccination by Mawhin's coincidence degree method. Some relevant numerical simulations are presented to illustrate the effectiveness of such pulse vaccination strategy. [ABSTRACT FROM AUTHOR]

In this paper, global dynamical properties of rational higher-order system are explored in the interior of ℝ + 3. It is explored that under certain parametric conditions, the discrete-time system has at most eight equilibria. By the method of linearization, local dynamics has been explored. It is explored that positive solution of the system is bounded, and moreover fixed point P 000 is globally stable if α 1 / α 2 < 1 , α 4 / α 5 < 1 , α 7 / α 8 < 1. It is also investigated that the positive solution of the system under consideration converges to P 000 . Lastly, theoretical results are confirmed by numerical simulation. The presented work is significantly extended and improves current results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the asymptotic behavior of a multigroup SEIR model with stochastic perturbations and nonlinear incidence rate functions is studied. First, the existence and uniqueness of the solution to the model we discuss are given. Then, the global asymptotical stability in probability of the model with R 0 < 1 is established by constructing Lyapunov functions. Next, we prove that the disease can die out exponentially under certain stochastic perturbation while it is persistent in the deterministic case when R 0 > 1. Finally, several examples and numerical simulations are provided to illustrate the dynamic behavior of the model and verify our analytical results. [ABSTRACT FROM AUTHOR]

Synchronization of multilayer complex networks is one of the important frontier issues in network science. In this paper, we strictly derived the analytic expressions of the eigenvalue spectrum of multilayer star and star-ring networks and analyzed the synchronizability of these two networks by using the master stability function (MSF) theory. In particular, we investigated the synchronizability of the networks under different interlayer coupling strength, and the relationship between the synchronizability and structural parameters of the networks (i.e., the number of nodes, intralayer and interlayer coupling strengths, and the number of layers) is discussed. Finally, numerical simulations demonstrated the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

Synchronization of multilayer complex networks is one of the important frontier issues in network science. In this paper, we strictly derived the analytic expressions of the eigenvalue spectrum of multilayer star and star-ring networks and analyzed the synchronizability of these two networks by using the master stability function (MSF) theory. In particular, we investigated the synchronizability of the networks under different interlayer coupling strength, and the relationship between the synchronizability and structural parameters of the networks (i.e., the number of nodes, intralayer and interlayer coupling strengths, and the number of layers) is discussed. Finally, numerical simulations demonstrated the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

The reaction diffusion system is one of the important models to describe the objective world. It is of great guiding importance for people to understand the real world by studying the Turing patterns of the reaction diffusion system changing with the system parameters. Therefore, in this paper, we study Gierer–Meinhardt model of the Depletion type which is a representative model in the reaction diffusion system. Firstly, we investigate the stability of the equilibrium and the Hopf bifurcation of the system. The result shows that equilibrium experiences a Hopf bifurcation in certain conditions and the Hopf bifurcation of this system is supercritical. Then, we analyze the system equation with the diffusion and study the impacts of diffusion coefficients on the stability of equilibrium and the limit cycle of system. Finally, we perform the numerical simulations for the obtained results which show that the Turing patterns are either spot or stripe patterns. [ABSTRACT FROM AUTHOR]

In this paper, the discontinuous Galerkin (DG) method is applied to solve the governing equations of the dispersed two-phase flow with the two-fluid Euler/Euler approach. The resulting governing equations are simple in form and the solution process is very natural. The characteristics of the gas-particle two-phase flow in an engine nozzle are mainly analyzed, and the impacts of the particle mass fraction and particle size on the flow field and engine performance are evaluated. Because of the addition of particles, the gas flow field undergoes significant modifications. Increase in the mass fraction leads to a significant thrust loss in the gas phase, and the impact of the particles on the gas phase could be substantial. Therefore, a quantitative study of thrust loss in the nozzle due to the particle impact is made. It is found that the gas thrust in the two-phase flow is reduced, but the total thrust of the two-phase flow increases to a certain extent. [ABSTRACT FROM AUTHOR]

This paper is concerned with the mean-square exponential input-to-state stability problem for a class of stochastic Cohen-Grossberg neural networks. Different from prior works, neutral terms and mixed delays are discussed in our system. By employing the Lyapunov-Krasovskii functional method, Itô formula, Dynkin formula, and stochastic analysis theory, we obtain some novel sufficient conditions to ensure that the addressed system is mean-square exponentially input-to-state stable. Moreover, two numerical examples and their simulations are given to illustrate the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers a stochastic delay Gilpin-Ayala model with Markovian switching. Using Lyapunov method, we show existence and uniqueness of global positive solution. Then, by using Chebyshev's inequality, M-matrix method, and BDG's inequality, stochastic permanence and asymptotic estimations of solutions are studied. Finally, numerical simulations illustrate the theoretical results. Our results generalize and improve the existing results. [ABSTRACT FROM AUTHOR]

In this paper, a discrete predator-prey system with the periodic boundary conditions will be considered. First, we get the conditions for producing Turing instability of the discrete predator-prey system according to the linear stability analysis. Then, we show that the discrete model has the flip bifurcation and Turing bifurcation under the critical parameter values. Finally, a series of numerical simulations are carried out in the Turing instability region of the discrete predator-prey model; some new Turing patterns such as striped, bar, and horizontal bar are observed. [ABSTRACT FROM AUTHOR]

This paper proposes a novel impulsive stochastic nonautonomous chemostat model with the saturated and bilinear growth rates in a polluted environment. Using the theory of impulsive differential equations and Lyapunov functions method, we first investigate the dynamics of the stochastic system and establish the sufficient conditions for the extinction and the permanence of the microorganisms. Then we demonstrate that the stochastic periodic system has at least one nontrivial positive periodic solution. The results show that both impulsive toxicant input and stochastic noise have great effects on the survival and extinction of the microorganisms. Furthermore, a series of numerical simulations are presented to illustrate the performance of the theoretical results. [ABSTRACT FROM AUTHOR]

The application of pest management involves two thresholds when the chemical control and biological control are adopted, respectively. Our purpose is to provide an appropriate balance between the chemical control and biological control. Therefore, a Smith predator-prey system for integrated pest management is established in this paper. In this model, the intensity of implementation of biological control and chemical control depends linearly on the selected control level (threshold). Firstly, the existence and uniqueness of the order-one periodic solution (i.e., OOPS) are proved by means of the subsequent function method to confirm the feasibility of the biological and chemical control strategy of pest management. Secondly, the stability of system is proved by the limit method of the successor points' sequences and the analogue of the Poincaré criterion. Moreover, an optimization strategy is formulated to reduce the total cost and obtain the best level of pest control. Finally, the numerical simulation of a specific model is performed. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study and investigate the optimal control strategy of a discrete mathematical model of smoking with specific saturated incidence rate. The population that we are going to study is divided into five compartments: potential smokers, light smokers, heavy smokers, temporary quitters of smoking, and permanent quitters of smoking. Our objective is to find the best strategy to reduce the number of light smokers, heavy smokers, and temporary quitters of smoking. We use three control strategies which are awareness programs through media and education, treatment, and psychological support with follow-up. Pontryagins maximum principle in discrete time is used to characterize the optimal controls. The numerical simulation is carried out using MATLAB. Consequently, the obtained results confirm the performance of the optimization strategy. [ABSTRACT FROM AUTHOR]

MiR-17-92 plays an important role in regulating the levels of the Myc/E2F protein. In this paper, we consider a coupling network between Myc/E2F/miR-17-92 delayed negative feedback loop and Myc/E2F positive feedback loop described by a two-dimensional delay differential equation. Based on linear stability analysis and bifurcation theory, sufficient conditions for stability of equilibria and oscillatory behaviors via Hopf bifurcation are derived when choosing time delay as well as negative feedback strength associated with oscillations as bifurcation parameters, respectively. Furthermore, direction and stability of Hopf bifurcation of time delay are studied by using the normal form method and center manifold theorem. Finally, several numerical simulations are performed to verify the results we obtained. [ABSTRACT FROM AUTHOR]

Based on integrating the fundamental attribute and the unique property of the collaborative innovation network, this paper establishes a collaborative innovation network model of Artificial Intelligence industry through depicting external stimulus conversion progresses and behaviors of network heterogeneous agents. Heterogeneous agents are the network elements of the model which regards the stimulus response as the evolutionary mechanism. Tencent is one of the largest Internet integrated service providers and one of the Internet companies with the largest number of service users in China, which has also set its sights on the development of the AI industry. Taking Tencent’s patent cooperation network in the field of Artificial Intelligence as an example and using system simulation method, we analyze the evolutionary law of the collaborative innovation network topology structure, the coupling evolution phenomenon of the knowledge and the network topology structure, distinct roles that agents play in the network, and relationship between the agents’ openness and the knowledge flow efficiency. We find the phenomenon of small world emergence more than once through the evolution of collaborative innovation network, whose degrees and reasons are also distinctive. There exists coupling evolution between the technological knowledge and the network structure. The collaborative innovation network is always oriented towards competitive industries. The agents’ openness has an essential influence on the lifting range of the technological knowledge. Strengthening the main position of enterprises in AI technological innovation and enhancing the degree of openness among heterogeneous agents are a powerful guarantee for improving the performance of collaborative innovation. [ABSTRACT FROM AUTHOR]

In this paper, the impact of the fusion framework on the fault diagnosis process is discussed. The centralized fusion framework makes it difficult to locate and estimate the sensor fault. Based on the fault detection method, the sequential fusion framework could locate and estimate the sensor fault and realize the fault-tolerant estimation of system states. In the sense of minimum mean square error (MMSE), based on the sequential detection of bias fault of sensors, a sequential fault-tolerant fusion estimation approach is presented to estimate the sensor fault and the system state, simultaneously, optimally, in real time. Further, a novel alternate fault-tolerant fusion estimation method is proposed to alternately estimate the sensor fault and the system state, in the frame of sequential fusion. What is more, the equivalency of the two proposed methods is proved. And the feasibility and equivalency of them are also verified by the computer simulation. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an SLBRS computer virus model with time delay and impact of antivirus software. The proposed model considers the entering rates of all computers since every computer can enter or leave the Internet easily. It has been observed that there is a stability switch and the system becomes unstable due to the effect of the time delay. Conditions under which the system remains locally stable and Hopf bifurcation occurs are found. Sufficient conditions for global stability of endemic equilibrium are derived by constructing a Lyapunov function. Formulae for the direction, stability, and period of the bifurcating periodic solutions are conducted with the aid of the normal form theory and center manifold theorem. Numerical simulations are carried out to analyze the effect of some of the parameters in the system on the dynamic behavior of the system. [ABSTRACT FROM AUTHOR]

In this paper, we propose a chemostat model of competition between plasmid-bearing and plasmid-free organism with the impulsive state feedback control. The sufficient condition for existence of the positive period-1 solution is obtained by means of successor function and the qualitative properties of the corresponding continuous system. We show that the impulsive control system is more effective than the corresponding continuous system if we choose a suitable threshold value of the state feedback control in the process of manufacturing the desired products through genetically modified techniques. Furthermore, a new method of proving the stability of the order-1 periodic solution is given based on the theory of the limit cycle of the continuous dynamical system. Finally, mathematical results are justified by some numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel Holling-Tanner model with impulsive control and then provide a detailed qualitative analysis by using theories of impulsive dynamical systems. The Poincaré map is first constructed based on the phase portraits of the model. Then the main properties of the Poincaré map are investigated in detail which play important roles in the proofs of the existence of limit cycles, and it is concluded that the definition domain of the Poincaré map has a complicated shape with discontinuity points under certain conditions. Subsequently, the existence of the boundary order-1 limit cycle is discussed and it is shown that this limit cycle is unstable. Furthermore, the conditions for the existence and stability of an order-1 limit cycle are provided, and the existence of order-k(k≥2) limit cycle is also studied. Moreover, numerical simulations are carried out to substantiate our results. Finally, biological implications related to the mathematical results which are beneficial for successful pest control are addressed in the Conclusions section. [ABSTRACT FROM AUTHOR]

This paper proposes a new fractional-order chaotic system with five terms. Firstly, basic dynamical properties of the fractional-order system are investigated in terms of the stability of equilibrium points, Jacobian matrices theoretically. Furthermore, rich dynamics with interesting characteristics are demonstrated by phase portraits, bifurcation diagrams numerically. Besides, the control problem of the new fractional-order system is discussed via numerical simulations. Our results demonstrate that the new fractional-order system has compound structure. [ABSTRACT FROM AUTHOR]

In Cournot model, when there are many competitions, the competitive equilibrium becomes chaotic. It is extremely difficult to derive the general equilibrium points. There is no previous research to explore a further problem with the general equilibrium points of n-contenders in Cournot model. In this paper, a general equilibrium Cournot game is proposed based on an inverse demand function. A market spatial structure model is built. Intermediate value theorem, as a realistic method, is introduced to handle a general competitive equilibrium in Cournot model. The number and stability in general equilibrium points are detected by means of celestial motion theory and spatial agglomeration competition model. The existence of general equilibrium points and the stability of Cournot equilibrium points, which are new and future complement of previously known results. Numerical simulations are given to support the research results. [ABSTRACT FROM AUTHOR]

Based on an integer-order Brushless DC motors (IO-BLDCM) system, we give a fractional-order Brushless DC motors (FO-BLDCM) system in this paper. There exists a chaotic attractor for fractional-order 0.95

The mine logistics transportation system with belt and surge links is often formed by a complex hybrid dynamic system that consists of continuous and discrete links, and these parts can have the complex changes along with the mining engineering going on. Studying the hybrid system with belt and surge links to fully realize its beneficial functions is very significant. Until now, there have been many references studying the logistics transportation hybrid system with belt and surge links, and many concepts about it have been set up. However, in these references, complicated real-time dynamic changes of the hybrid system usually is studied. This paper presents a novel approach to study real-time dynamic optimization analysis and simulation problems of complex mine logistics transportation hybrid system, which can be used to make optimization design for this kind of complex hybrid system. The proposed method considered expressly complicated real-time dynamic changing of the hybrid system comparing with some existing references and can solve some optimization design problems of the hybrid system. In addition, this paper used statistical data of a real logistics transportation system with belt and surge bin on simulation and gets some useful conclusions. The application result shows that the presented method is valid. [ABSTRACT FROM AUTHOR]

This paper concerns a stochastic Lotka-Volterra model with two predators competing for one prey. The sufficient conditions which guarantee the principle of competitive exclusion for this perturbed model are given by using Lyapunov analysis methods. Numerical simulations for a set of parameter values are presented to illustrate the analytical findings. [ABSTRACT FROM AUTHOR]

The avian influenza A(H7N9) virus has certain fatal effects on human. In this paper, a mathematical model describing the transmission dynamics of avian influenza A(H7N9) between human and poultry is investigated. The basic reproduction number of the model is obtained by applying the method of the next generation matrix. Then the local and global stability of the equilibria are proven. At last, we use numerical simulations to verify the theoretical results. [ABSTRACT FROM AUTHOR]

We present in this paper an investigation on a discrete predator-prey system with Crowley-Martin type functional response to know its complex dynamics on the routes to chaos which are induced by bifurcations. Via application of the center manifold theorem and bifurcation theorems, occurrence conditions for flip bifurcation and Neimark-Sacker bifurcation are determined, respectively. Numerical simulations are performed, on the one hand, verifying the theoretical results and, on the other hand, revealing new interesting dynamical behaviors of the discrete predator-prey system, including period-doubling cascades, period-2, period-3, period-4, period-5, period-6, period-7, period-8, period-9, period-11, period-13, period-15, period-16, period-20, period-22, period-24, period-30, and period-34 orbits, invariant cycles, chaotic attractors, sub-flip bifurcation, sub-(inverse) Neimark-Sacker bifurcation, chaotic interior crisis, chaotic band, sudden disappearance of chaotic dynamics and abrupt emergence of chaos, and intermittent periodic behaviors. Moreover, three-dimensional bifurcation diagrams are utilized to study the transition between flip bifurcation and Neimark-Sacker bifurcation, and a critical case between the two bifurcations is found. This critical bifurcation case is a combination of flip bifurcation and Neimark-Sacker bifurcation, showing the nonlinear characteristics of both bifurcations. [ABSTRACT FROM AUTHOR]