Bifurcation and Turing Pattern Formation in a Diffusion Modified Leslie-Gower Predator-Prey Model with Crowley-Martin Functional Response

In this paper, we study a modified Leslie-Gower predator-prey model with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is the Crowley-Martin functional response term. Firstly, for ODE model, the local stability of equilibrium point is given. And by using bifurcation theory and selecting suitable bifurcation parameters, we find many kinds of bifurcation phenomena, including Transcritical bifurcation and Hopf bifurcation. For the reaction-diffusion model, we find that Turing instability occurs. Besides, it is proved that Hopf bifurcation exists in the model. Finally, numerical simulations are presented to verify and illustrate the theoretical results.

THE QUALITATIVE ANALYSIS OF A TWO SPECIES AMENSALISM MODEL WITH NON-MONOTONIC FUNCTIONAL RESPONSE AND ALLEE EFFECT ON SECOND SPECIES

In this paper, we present a two species amensalism model with non-monotonic functional response and Allee effect on second species. Local and global stability of the boundary and interior equilibrium are investigated. By introducing the Allee effect, we show that the boundary equilibrium have changed from unstable node and saddle into saddle-node. Also, the system subject to an Allee effect has increased the time of reach to its stable steady-state solution, but has no influence on the final density of the two species. Our results are supported by numeric simulations.

Stability Analysis of a Self-Memory Prey-Predator Diffusion Model Based on Bazykin Functional Response

To investigate the effects of self-memory diffusion on predator-prey models, we consider a predator-prey model with Bazykin functional response of self- memory diffusion. The uniqueness, boundedness, positivity, existence and stability of equilibrium point of the model are studied. In this paper, the uniqueness of the solution is discussed under the non-negative initial function and Neumann boundary conditions satisfying a specific space. The boundness of the solution is proved by the comparison principle of parabolic equations, and the positivity of the solution is proved by the strong maximum principle of parabolic equations. Hurwitz criterion and Lyapunov function construction are used to analyze the local stability and global stability of feasible equilibrium points. The results show that the system solution is unique non-negative and bounded. The model is unstable at the trivial equilibrium point E0 and the boundary equilibrium point E1, and the condition of whether the positive equilibrium point E2 is stable under certain conditions is given.

Dynamic Analysis of a Predator-Prey Model with Holling-II Functional Response

A predator-prey model with linear capture term Holling-II functional response was studied by using differential equation theory. The existence and the stabilities of non-negative equilibrium points of the model were discussed. The results show that under certain limited conditions, these two groups can maintain a balanced position, which provides a theoretical reference for relevant departments to make decisions on ecological protection.

Inflammation: Complexity and significance of cellular and molecular responses

Inflammation is a multifaceted cellular and molecular response triggered by injury,infection,or various pathological conditions.Serving as a protective defense mechanism,the inflammatory response involves clinical signs like redness,swelling,pain,and increased body temperature.Immune cells,notably neutrophils and macrophages,play key roles in orchestrating this response.The delicate balance between proinflammatory and anti-inflammatory mediators,including cytokines and chemokines,regulates the inflammatory cascade.While acute inflammation is crucial for tissue repair,chronic inflammation may indicate an imbalance,contributing to conditions like autoimmune diseases.Understanding these mechanisms is vital for developing therapeutic strategies and managing chronic diseases.

Improvement of inflammatory response and gastrointestinal function in perioperative of cholelithiasis by Modified Xiao-Cheng-Qi decoction

BACKGROUND In the perioperative period of biliary surgery,various factors can induce the release of a large number of inflammatory factors,leading to an imbalance in proinflammatory and anti-inflammatory responses and resulting in gastrointestinal(GI)dysfunction.Enhanced Recovery After Surgery protocols in biliary surgery have been shown to reduce the stress response and accelerate postoperative recovery.It is crucial to reduce the inflammatory response and promote the recovery of GI function after biliary surgery,both of which are the basis and key for perioperative care and postoperative recovery.AIM To better understand the effects of Modified Xiao-Cheng-Qi decoction(MXD)on inflammatory response and GI function in the perioperative management of cholelithiasis and their correlation.METHODS This was a prospective randomized placebo-controlled trial,in which 162 patients who received biliary tract surgery were randomly assigned to three groups:MXD group,XD group,and placebo-control group.The observed parameters included frequency of bowel sounds,time of first flatus and defecation,time of diet,and amount of activity after surgery.The serum levels of C-reactive protein(CRP),interleukin(IL)-6,IL-10,serum amyloid A protein(SAA),and substance P were measured by the enzyme-linked immunosorbent assay.Then,the spearman correlation coefficient was used to analyze the relationship between the indicators of GI function and inflammation.RESULTS Compared to the placebo-control,improvements in GI function were observed in the MXD groups including reduced incidence of nausea,vomiting,and bloating;and earlier first exhaust time,first defecation time,and feeding time after surgery(P<0.05).On the 1st and 2nd d after surgery,IL-6,CRP and SAA levels in MXD group were lower than that in placebo control,but substance P level was higher,compared to the control(P<0.05).Functional diarrhea occurred in both MXD and XD groups without any other adverse effects,toxic reactions,and allergic reactions.Diarrhea was relieved after the discontinuation of the investigational remedies.Bowel sounds at 12 h after surgery,the occurring time of the first flatus,first defecation,postoperative liquid diet and semiliquid diet were significantly correlated with levels of IL-6,CRP,SAA and substance P on second day after surgery(P<0.05).CONCLUSION Treatment with MXD can relieve inflammatory response and improve GI function after surgery.Moreover,there are significant correlations between them.Furthermore,it does not cause serious adverse reactions.

Improvement of a temperature response function for divertor heat flux monitoring in fusion devices

Temperature response functions have been developed to investigate sensor design and divertor heat flux estimation in magnetically confined plasmas. The time-dependent heat flux can be derived by fitting the response function to experimental thermocouple(TC) data. Because the TC signals have a time delay to transit events such as discharge start or confinement transition, the time delay is taken into account in a temperature response function. Such a function accurately describes the signal from each TC channel with time delay in a sensor test using a neutral beam injection. Measurement for commercial TCs shows that the time delay is caused by the finite heat capacity of TC wire and contact heat resistance between TC and target surface.

EXISTENCE OF POSITIVE SOLUTION FOR A TWO-PATCHES COMPETITION SYSTEM WITH DIFFUSION AND TIME DELAY AND FUNCTIONAL RESPONSE

By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]′ 1 (t)=x 1(t)a 1(t)-b 1(t)x 1(t)-c 1(t)y(t)1+m(t)x 1(t)+D 1(t)[x 2(t)-x 1(t)], x [FK(W1*3/4。*2/3]′ 2 (t)=x 2(t)a 2(t)-b 2(t)x 2(t)-c 2(t)∫ 0 -τ k(s)x 2(t+s) d s+D 2(t)[x 1(t)-x 2(t)], y′(t)=y(t)a 3(t)-b 3(t)y(t)-c 3(t)x 1(t)1+m(t)x 1(t)is established, where a i(t),b i(t),c i(t)(i=1,2,3),m(t) and D i(t)(i=1,2) are all positive periodic continuous functions with period w >0, τ is a nonnegative constant and k(s) is a continuous nonnegative function on [- τ ,0].

Mechanism of Functional Responses to Loading of Carbon Fiber Reinforced Cement-based Composites

Single fiber pull-out testing was conducted to study the origin of the functional responses to loading of carbon fiber reinforced cement-based composites. The variation of electrical resistance with the bonding force on the fiber-matrix interface was measured. Single fiber electromechanical testing was also conducted by measuring the electrical resistance under static tension. Comparison of the results shows that the resistance increasing during single fiber pull-out is mainly due to the changes at the interface. The conduction mechanism of the composite can be explained by the tunneling model. The interfacial stress causes the deformation of interfacial structure and the interfacial debonding, which have influences on the tunneling effect and result in the change of resistance.

Effects of Temperature on Functional Response of Anagrus nilaparvatae Pang et Wang (Hymenoptera:Mymaridae) on the Eggs of Whitebacked Planthopper,Sogatella furcifera Horvth and Brown Planthopper,Nilaparvata lugens Stl

Understanding the temperature affecting parasitic efficiency is critical to succeed in utilizing parasitoid as natural enemy in pest management. Laboratory studies were carried out to determine the effects of temperature on parasitoid preference of female Anagrus nilaparvatae Pang et Wang （Hymenoptera：Mymaridae） to the eggs of whitebacked planthopper （WBPH）, Sogatella furcifera Horváth and brown planthopper （BPH）, Nilaparvata lugens Stl to build a composite model describing changes in parasitic response along a temperature gradient （18, 22, 26, 30, 34°C）. The results showed that attack responses of A. nilaparvatae on WBPH and BPH were the best described by a Type II functional response. The two parameters, attack rates （a） and handling times （Th）, of A. nilaparvatae to both eggs were influenced by the temperature. The maximum attack rates to WBPH （1.235） and BPH （1.049） were at 26 and 34°C, respectively, and the shortest handling times to WBPH （0.063） and BPH （0.057） were at 30 and 26°C, respectively. However, the optimal temperature for parasitic efficiency of A. nilaparvatae to WBPH and BPH eggs was both at 26°C, which showed that the present microclimate temperature of the habitat in the paddyfield was beneficial to A. nilaparvatae and indicated that parasitic efficiency of A. nilaparvatae would be impaired by global warming.

Tool Condition Monitoring Based on Nonlinear Output Frequency Response Functions and Multivariate Control Chart

Tool condition monitoring(TCM)is a key technology for intelligent manufacturing.The objective is to monitor the tool operation status and detect tool breakage so that the tool can be changed in time to avoid significant damage to workpieces and reduce manufacturing costs.Recently,an innovative TCM approach based on sensor data modelling and model frequency analysis has been proposed.Different from traditional signal feature-based monitoring,the data from sensors are utilized to build a dynamic process model.Then,the nonlinear output frequency response functions,a concept which extends the linear system frequency response function to the nonlinear case,over the frequency range of the tooth passing frequency of the machining process are extracted to reveal tool health conditions.In order to extend the novel sensor data modelling and model frequency analysis to unsupervised condition monitoring of cutting tools,in the present study,a multivariate control chart is proposed for TCM based on the frequency domain properties of machining processes derived from the innovative sensor data modelling and model frequency analysis.The feature dimension is reduced by principal component analysis first.Then the moving average strategy is exploited to generate monitoring variables and overcome the effects of noises.The milling experiments of titanium alloys are conducted to verify the effectiveness of the proposed approach in detecting excessive flank wear of solid carbide end mills.The results demonstrate the advantages of the new approach over conventional TCM techniques and its potential in industrial applications.

The Dynamical Behavior of a Certain Predator-Prey System with Holling Type II Functional Response

In this paper we analytically and numerically consider the dynamical behavior of a certain predator-prey system with Holling type II functional response, including local and global stability analysis, existence of limit cycles, transcritical and Hopf bifurcations. Mathematical theory derivation mainly focuses on the existence and stability of equilibrium point as well as threshold conditions for transcritical and Hopf bifurcation, which can in turn provide a theoretical support for numerical simulation. Numerical analysis indicates that theoretical derivation results are correct and feasible. In addition, it is successful to show that the dynamical behavior of this predator-prey system mainly depends on some critical parameters and mathematical relationships. All these results are expected to be meaningful in the study of the dynamic complexity of predatory ecosystem.

The Dynamical Behavior of a Predator-Prey System with Holling Type II Functional Response and Allee Effect

In this paper, we mainly considered the dynamical behavior of a predator-prey system with Holling type II functional response and Allee-like effect on predator, including stability analysis of equilibria and Hopf bifurcation. Firstly, we gave some sufficient conditions to guarantee the existence, the local and global stability of equilibria as well as non-existence of limit cycles. By using the cobweb model, some cases about the existence of interior equilibrium are also illustrated with numerical outcomes. These existence and stability conclusions of interior equilibrium are also suitable in corresponding homogeneous reaction-diffusion system subject to the Neumann boundary conditions. Secondly, we theoretically deduced that our system has saddle-node bifurcation, transcritical bifurcation and Hopf bifurcation under certain conditions. Finally, for the Hopf bifurcation, we choose d as the bifurcation parameter and presented some numerical simulations to verify feasibility and effectiveness of the theoretical derivation corresponding to the existence of yk, respectively. The Hopf bifurcations are supercritical and limit cycles generated by the critical points are stable.

Predictive functional control of integrating process based on impulse response

The predictive model is built according to the characteristics of the impulse response of integrating process. In order to eliminate the permanent offset between the setpoint and the process output in the presence of the load disturbance, a novel error compensation method is proposed. Then predictive functional control of integrating process is designed. The method given generates a simple control structure, which can significandy reduce online computation. Furthermore, the tuning of the controller is fairly straightforward. Simulation results indicate that the designed control system is relatively robust to the parameters variation of the process.

Global Asymptotic Stability and Hopf Bifurcation in a Homogeneous Diffusive Predator-Prey System with Holling Type II Functional Response

In this paper, we considered a homogeneous reaction-diffusion predator-prey system with Holling type II functional response subject to Neumann boundary conditions. Some new sufficient conditions were analytically established to ensure that this system has globally asymptotically stable equilibria and Hopf bifurcation surrounding interior equilibrium. In the analysis of Hopf bifurcation, based on the phenomenon of Turing instability and well-done conditions, the system undergoes a Hopf bifurcation and an example incorporating with numerical simulations to support the existence of Hopf bifurcation is presented. We also derived a useful algorithm for determining direction of Hopf bifurcation and stability of bifurcating periodic solutions correspond to j &#8800;0 and j = 0, respectively. Finally, all these theoretical results are expected to be useful in the future study of dynamical complexity of ecological environment.

Board-invited review: Sensitivity and responses of functional groups to feed processing methods on a molecular basis

In complex feed structures, there exist main chemical functional groups which are associated with nutrient utilization and availability and functionality. Each functional group has unique molecular structure therefore produce unique molecular vibration spectral profile. Feed processing has been used to improve nutrient utilization for many years. However, to date, there was little study on processing-induced changes of feed intrinsic structure and functional groups on a molecular basis within intact tissue. This is because limited research technique is available to study inherent structure on a molecular basis. Recently bioanalytical techniques： such as Synchrotron Infrared Microspectroscopy as well as Diffuse Reflectance Infrared Fourier Transform molecular spectroscopy have been developed. These techniques enable to detect molecular structure change within intact tissues. These techniques can prevent destruction or alteration of the intrinsic protein structures during processing for analysis. However, these techniques have not been used in animal feed and nutrition research. The objective of this review was show that with the advanced technique, sensitivity and responses of functional groups to feed processing on a molecular basis could be detected in my research team. These functional groups are highly associated with nutrient utilization in animals.

Non-Monotonic Lyapunov-Krasovskii Functional Approach to Stability Analysis and Stabilization of Discrete Time-Delay Systems

In this paper, a novel non-monotonic Lyapunov-Krasovskii functional approach is proposed to deal with the stability analysis and stabilization problem of linear discrete time-delay systems. This technique is utilized to relax the monotonic requirement of the Lyapunov-Krasovskii theorem. In this regard, the Lyapunov-Krasovskii functional is allowed to increase in a few steps, while being forced to be overall decreasing. As a result, it relays on a larger class of Lyapunov-Krasovskii functionals to provide stability of a state-delay system. To this end, using the non-monotonic Lyapunov-Krasovskii theorem, new sufficient conditions are derived regarding linear matrix inequalities(LMIs)to study the global asymptotic stability of state-delay systems.Moreover, new stabilization conditions are also proposed for time-delay systems in this article. Both simulation and experimental results on a p H neutralizing process are provided to demonstrate the efficacy of the proposed method.

The Global Stability of Predator-Prey System of Gause-Type with Holling Ⅲ Functional Response

This paper deals with the questio n of global stability of the positive locally asymptotically stable equilibrium in a class of predator\|prey system of Gause\|typ e with Holling Ⅲ functional response. The Dulac's criterion is applied and lia punov functions are constructed to establish the global stability.

Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates

This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.

THERMAL AND THERMO-ELASTIC-PLASTIC RESPONSE OF CERAMIC-METAL FUNCTIONALLY GRADED MATERIALS—THERMAL SHOCK PROBLEM

The thermal and thermo-elastic-plastic response of newly developed ceramic-metal functionally graded materials under a thermal shock load is studied. The materials are heated at the ceramic surface with a sudden high-intensity heat flux input, and cooled at the metal surface with a flowing liquid nitrogen. Emphasis is placed on two aspects: (1) the influence of the graded composition of the materials on the temperature and stress response; and (2) the optimum design of the graded composition from a unified viewpoint of the heat insulation property and stress relaxation property. Moreover, a comparison between the thermoelastic stress and the thermo-elastic-plastic stress is also made to indicate the plasticity effect.