Search

The optimal parameter selection problem for the state dependent impulsive equations is a challenging problem since the impulse number and impulse moments are dependent on the control parameters implicitly. In the simple continuous case, the state variables are continuous with respect to the control parameter when the impulse number is fixed. We prove the existence of the optimal solution and present the gradient of the cost functional such that the optimal problem can be solved by some gradient based optimization methods. For the difficult discontinuous case, i.e., the unfixed impulse number, we construct an approximation problem, and prove that its optimal value converges to that of the original optimal problem by the definition of epi-convergence. Then the corresponding gradient and solving algorithm are given. Finally, two numerical examples are presented to show the efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

Abstract Considering planktonic ecosystem as the bottom trophic levels of aquatic food webs, we derive a nutrient–phytoplankton–zooplankton model with spatially averaged parameters, where zooplankton population with two age classes and a fixed maturation period lives in a spatially bounded environment. The model can be transformed into a reaction–diffusion equation with non-local delay. Such transformation allows us to use results readily available from comparison argument and persistence theory to study the global compact attractor of solution semiflow, global attractivity and globally asymptotical stability of steady states. Our results can be used to design the control strategy of harmful algal blooms which have caused large fish kills and millions of dollars in economic losses. [ABSTRACT FROM AUTHOR]

This paper mainly provides Hopf bifurcation formulas for a general Gause type predator–prey system with diffusion and Neumann boundary condition by using the center manifold theory and normal form method, where the spectral and stability analysis around an equilibrium is addressed, and our results can be applied to the case without diffusion. As an application of these results, we give a complete and rigorous analysis of the global dynamics of a diffusive predator–prey model with herd behavior, especially, the Hopf bifurcation and its direction, and the stability of the bifurcating periodic solutions. [ABSTRACT FROM AUTHOR]

This work proposes a nutrient–phytoplankton–zooplankton (NPZ) model which is governed by a partially degenerate reaction–diffusion equation. Due to the noncompactness of solution map, the Kuratowski measure is introduced to prove the existence of the global attractor. By an innovative construction of Lyapunov functions, sufficient conditions are given to obtain the global attractivity of steady states of the system with spatial parameters. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the existence of three types of traveling waves for a general predator–prey systems of Gause type: traveling wave train solution, point-to-point and point-to-periodic traveling wave solutions. Applying the methods of Wazewski theorem, LaSalle’s invariance principle and Hopf bifurcation theorem, we obtain the existence results. Also, the minimal wave speed for biological invasion is obtained. Furthermore, some applications are given to illustrate our results. [Copyright &y& Elsevier]

Abstract: In compared with specialist predators which feed almost exclusively on a specific species of prey, generalist predators feed on many types of species. Consequently, their dynamics is not coupled to the dynamics of a specific prey population, and the generalist predators has itself growth function which be extended a well-known logistic growth term. We develop a generalist predator–prey model with diffusion and study the effect of harvesting and delay under Neumann conditions. The stability of the equilibria is firstly investigated, and the existence of traveling wave solutions is then established by constructing a pair of upper–lower solutions and using the cross iteration method and Schauder’s fixed point theorem. [Copyright &y& Elsevier]

Abstract: This paper deals with a predator–prey model with specialist harvesting, representing a two predators (Zooplankton) and one resource (Phytoplankton) system. First, the existence and stability of equilibria is analyzed both from local and global point of view. Our results indicate that a specialist harvesting which is discriminate may mediate the coexistence of the two zooplankton species which competitively exclude each other in absence harvesting. Although in most cases increasing harvesting reduces the two zooplankton species numbers, when harvesting leads to coexistence, it may also lead to increase the two zooplankton species numbers. Furthermore, to protect fish population from over exploitation a control instrument tax is imposed. The problem of optimal taxation policy is then solved by using Pontryagin’s maximal principle. It is established that the zero discounting leads to the maximization of the net economic revenue to the society and an infinite discount rate leads to complete dissipation of the net economic revenue to the society. Finally, the impact of harvesting is mentioned along with numerical results to provide some support to the analytical findings. [Copyright &y& Elsevier]

Abstract: In a natural ecosystem, specialist predators feed almost exclusively on one species of prey. But generalist predators feed on many types of species. Consequently, their dynamics is not coupled to the dynamics of a specific prey population. However, the defense of prey formed by congregating made the predator tend to move in the direction of lower concentration of prey species. This is described by cross-diffusion in a generalist predator–prey model. First, the positive equilibrium solution is globally asymptotically stable for the ODE system and for the reaction–diffusion system without cross-diffusion, respectively, hence it does not belong to the classical Turing instability scheme. But it becomes linearly unstable only when cross-diffusion also plays a role. This implies that cross–diffusion can lead to the occurrence and disappearance of the instability. Our results exhibit some interesting combining effects of cross-diffusion, predations and intra-species interactions. Furthermore, we consider the existence and non-existence results concerning non-constant positive steady states (patterns) of the system. We demonstrate that cross-diffusion can create non-constant positive steady-state solutions. [Copyright &y& Elsevier]

Abstract: Considering that over exploitation would result in the extinction of the population, we propose and investigate a Holling II functional response prey-predator model with harvesting for fishery resource in a two-patch environment: a free fishing zone (patch 1) and a reserve zone (patch 2) where fishing is strictly prohibited. First, the presence of harvesting can impact the existence of equilibria. Further, stability criteria of the model is analyzed both from local and global point of view. Our results indicate that so long as the prey population in the reserved zone does not extinct, the both prey always exist, that is marine reserves should ensure the sustainability of system. Thus, marine reserves not only protect species inside the reserve area but they can also increase fish abundance in adjacent areas. Next, the existence of bionomic equilibrium and the optimal harvesting policy are discussed. The present value of revenues is maximized by using Pontryagin’s maximum principle. It is established that an infinite discount rate leads to complete dissipation of economic rent. Finally, some numerical simulations are given to illustrate our results. [Copyright &y& Elsevier]

Abstract: Considering the impact of harvesting on the coexistence and competitive exclusion of competitive predators, a two-zooplankton one-phytoplankton model with harvesting is proposed and investigated. First, stability criteria of the model is analyzed both from local and global point of view. Second, two types of zooplankton will competitively exclude each other in the absence of harvesting with the zooplankton with the larger threshold persisting. If harvest rates are discriminate, then a dominant zooplankton may occur depending on the harvesting level. Thus, for some harvesting levels, the zooplankton one may persist while for other harvesting levels zooplankton two may persist. Furthermore, the value of the harvesting level and coexistence line are obtained when coexistence occur. Finally, the impact of harvesting is mentioned along with numerical results to provide some support to the analytical findings. [Copyright &y& Elsevier]

Abstract: Considering that some phytoplankton and zooplankton are harvested for food, a phytoplankton–zooplankton model with harvesting is proposed and investigated. First, stability conditions of equilibria and existence conditions of a Hopf-bifurcation are established. Our results indicate that over exploitation would result in the extinction of the population and an appropriate harvesting strategy should ensure the sustainability of the population which is in line with reality. Furthermore, the existence of bionomic equilibria and the optimal harvesting policy are discussed. The present value of revenues is maximized by using Pontryagin’s maximum principle subject to the state equations and the control constraints. We discussed the case of optimal equilibrium solution. It is found that the shadow prices remain constant over time in optimal equilibrium when they satisfy the transversality condition. It is established that the zero discounting leads to the maximization of economic revenue and that an infinite discount rate leads to complete dissipation of economic rent. Finally, some numerical simulations are given to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper deals with a general age-structured model with diffusion. The existence and uniqueness of solutions of the equivalent integral equation are obtained in light of the contraction mapping theorem. By taking the mosquito population growth as a motivating example, we derive a periodic stage-structured model with diffusion, intra-specific competition and periodic delay. Next, we show that the solution is globally bounded for the setup we chose. Then, the basic reproduction number R 0 for this model is introduced to establish the threshold dynamics on mosquito extinction and persistence in terms of R 0. In the case where intra-specific competition among immature individuals is ignored, the adult equation is decoupled from the full equations, and the global stability of the positive periodic solution is then obtained by introducing a suitable phase space on which the periodic semiflow is eventually strongly monotone and strictly subhomogeneous. [ABSTRACT FROM AUTHOR]

In this paper, we consider the optimal harvesting for a size-stage-structured population model. The main feature of this article is to study optimal harvesting, stage structure and body size at the same time in a single population system. At first, under appropriate assumptions, by the method of characteristic and simple changes of variables, we obtain the properties of solutions of our model, including the global existence and uniqueness, nonnegativity and boundedness. Then, we give several useful estimates about the solutions. Taking advantage of these estimates and relevant theory of functional analysis, we derive the existence of optimal harvesting strategy. Finally, a discussion of related problems is also presented. [ABSTRACT FROM AUTHOR]

The adhesion between a metal alloy and a polymer is the problem focus of fiber metal laminates (FMLs) utilization. In this study, the Schiff base complex was firstly tentatively utilized for the surface modification of Ti-6Al-4 V (TC4), in order for a bridge between TC4 and PEEK to be built. In addition, the TC4 plates were anodized for the synergistic effects between roughness and complex to be explored. Differently modified TC4 plate surfaces were analyzed through Fourier Transform Infrared Spectroscopy (FT-IR), Thermogravimetry/Differential Scanning Calorimetry (TG/DSC), Contact angle measurements (CA), Scanning Electron Microscopy (SEM), X-ray photoelectron spectroscopy (XPS) and Atomic force microscopy (AFM). Moreover, the adhesive strength was studied through single lap shear testing. It was evidenced that the Schiff base and the corresponding complex were successfully synthesized; furthermore, the complex was loaded on the TC4 plate surface through self-assembly. When the TC4 plates were anodized and loaded the Schiff base complex, single lap shear strength significantly increased, reaching to 47.49 MPa. This was a 53.89% growth compared to the anodized TC4 plate strengths. It was demonstrated that the Schiff base complex highly contributed to the adhesive strength through the multiple effects of coordination, hydrogen bonding interactions, mechanical interlocking and molecular entanglement. [ABSTRACT FROM AUTHOR]

Exopolysaccharide (EPS) plays an important role in plant growth-promoting bacteria (PGPB)-mediated enhancement of plant abiotic stress resistance. In this study, it is found that EPS from Pantoea alhagi NX-11 foliar sprayed at 20, 50, and 100 ppm could significantly enhance drought resistance of rice seedlings. The fresh weight and relative water content of EPS sprayed were increased. In addition, malondialdehyde content reduced while total chlorophyll, proline and soluble sugar content, prominent enhanced. Meanwhile, the antioxidant enzymes, CAT, POD and SOD, were also significantly increased. The drought resistance of rice was most pronounced at the 50 ppm EPS dose. For the sake of commercializing the gram-negative EPS-producing PGPB which were difficult to preserve, it is vital to improve the EPS yield. First, the carbon source, nitrogen source and inorganic salt were optimized. Subsequently, the effect of three oxygen vectors, which could increase the efficiency of oxygen mass transfer, on EPS yield was studied by response surface methodology. The maximum EPS yield (19.27 g/L) was obtained, which is 51.7% higher than the initial yield of 12.7 g/L. Overall, it may provide a new way for the industrialization of PGPB to increase the yield of EPS. • EPS from P. alhagi NX-11 foliar sprayed increased drought resistance of rice. • The drought resistance of rice was most pronounced at the 50 ppm EPS dose. • The oxygen vectors were added to increase the EPS yield. • A maximum EPS yield of 19.27 g/L was achieved after optimization. [ABSTRACT FROM AUTHOR]

• Solving the overdetermined equations to make full use of the received signals for better DOA estimation accuracy. • The arbitrary tetrahedral array can be hosted on various underwater platforms besides UG in a conformal way. • CRLB is derived as the function of SNR, integration time, signal bandwidth, frequency, array arrangement and DOA of signal. • Deriving the upper frequency limit as a function of the effective array aperture of the tetrahedral array. This study proposes a method for estimating the three-dimensional (3-D) direction of arrival (DOA) of low-frequency line spectra with an arbitrary tetrahedral array on a moving underwater platform, such as underwater glider (UG). First, we provide the theoretical derivations of the 3-D DOA estimation algorithm. Four sensors are matched pairwise without duplication and the time difference of arrival (TDOA) of each pair is estimated using the cross-spectral method. The geometric relation between the space coordinate vector of the paired sensors and direction vector of the incoming signal is combined with the TDOA to establish the overdetermined equations. The algorithm solves the overdetermined equations to obtain the azimuth and elevation of the line spectra, and exploits all the information from sensors to enhance the accuracy of DOA estimation. And the Cramer–Rao lower bound (CRLB) of an arbitrary tetrahedral array is derived as a function of the signal-to-noise ratio (SNR), integration time, signal bandwidth, frequency, array arrangement, and DOA of the signal. Second, simulations and a sea trial verify the feasibility of the 3-D DOA estimation algorithm using a tetrahedral array on a moving UG. Finally, several factors that influence the algorithm are analyzed, including the DOA of the source, frequency, SNR, sensor position error and phase error. The upper frequency limit to avoid spatial aliasing is also derived as a function of the array aperture. The study shows that the tetrahedral array is suitable for various underwater mobile platforms owing to its small scale and irregularity. [ABSTRACT FROM AUTHOR]

The present work is to investigate fracture toughness of titanium-PEEK by linking the interface fracture toughness to surface parameters of micro-pit on titanium panels during delamination. The relationship between geometrical parameters and failure mechanisms is also explained. The regular micro-pits were fabricated on pure titanium panels by Lithography. The effects of micro-pattern on fracture toughness were systematically evaluated by changing geometrical parameters of surface topography. The results showed that by changing the parameters of surface pattern, the fracture toughness can be manipulated through plastic deformation and molecular bond breaking of PEEK. The optimized wetting angle and surface free energy, having influenced on the real contact area and the stress regions, were obtained by adjusting the geometrical parameters. Finally, it was found that the failure mechanism transition from interface to cohesive was because of the attributed optimal parameters, showing more energy dissipation. [ABSTRACT FROM AUTHOR]

The present work studies the effects of annealing and anodizing an AA5083 sheet on the metal/composite laminate adhesion, mechanical properties and corrosion behavior of the seawater hygrothermal aged AA5083-carbon fiber/epoxy fiber-metal laminates (Al FMLs) for marine applications. The results reveal that annealing at 250 °C decreases the porosity and the pore size of the anodized film. Consequently, the mechanical properties of Al FML deteriorate and metal/composite laminate interface weakens. Moreover, the mechanical properties of AA5083 sheets and laminates deteriorate after hygrothermal ageing. The higher percentage decrease in the mechanical properties of the Al FML having non-annealed AA5083 layers compared to annealed AA5083 layers is due to the excessive corrosion of the non-annealed AA5083 layers. The anodized annealed AA5083 sheets show the least mass losses in the nitric acid mass loss test (NAMLT). The failure mechanism in non-aged Al FMLs is the fracture of the outer AA5083 and composite laminate layers, while in aged Al FMLs, metal/composite laminate and fiber/resin interfaces delaminate. [ABSTRACT FROM AUTHOR]

Yongzhen et al. (2010) describe a mathematical model of a scenario where a plant population is imported to a pest–predator system with an infected pest. Thus a plant–pest–predator eco-epidemiological model disturbed by an impulsive effect is proposed. First of all, the stability conditions of the susceptible pest-eradication periodic solution for eradicating the susceptible pest are investigated. Compared with the results in (Yongzhen et al., 2010), the presence of the plant population increases the cost of natural enemies as well as the demand for insecticide. In addition, we study the effect of the death rate of the infected pest on pest control in terms of evolution of virulence and the basic reproductive number. Results show that larger mortalities of the infected pest will lead to the frustrated invasion or the instability of susceptible pest-eradication periodic solutions. Next, we focus on the four kinds of optimal impulsive control strategies, biological control, chemical control, and integrated control with fixed period or variable period, to maximize the yields of plants at the terminal time with minimum efforts. All the optimal control problems are solved via a time scaling technique and a gradient-based optimization method. Our results show that two parameters, the amount of sprayed infective pest and the kill fraction of the susceptible pest, play a key role in improving the yield of the plants. In addition, for the four kinds of control strategies, our results also show that biological control is more effective than chemical control to achieve an optimal solution, and the last two strategies can produce higher yields than the first two control strategies. [ABSTRACT FROM AUTHOR]

Opioid addiction is a brain disease that severely harms society and personal health. Although the tremendous numbers of patients worldwide and emerged negative events, effective treatments for opioid addiction are still lacking. Neuropeptide Y (NPY) is one of the main orexigenic peptides that play vital roles in food intake and energy metabolism. However, increasing evidence indicates that NPY may have great potential in mediating reward effects and drug dependence. In the present study, we assessed the expression changes of NPY in the nucleus accumbens at different timepoints following morphine conditioned place preference (CPP) and investigated the functional importance of potential NPY changes. Our results showed that NPY expression significantly decreased in the nucleus accumbens shell (AcbSh) immediately after chronic morphine exposure. Subsequently, it increased rapidly at first and then gradually returned to normal levels. Further data indicated that these NPY changes were involved in morphine reward memory, demonstrated by a reduction in the extinction period after blocking of the Y5 receptor by L-152,804 in the AcbSh and a prolonged duration of the extinction period following the application of NPY. More importantly, the additional results revealed that L-152,804 also remarkably suppressed the reinstatement of morphine CPP. Together, our results indicate that a complicated plasticity of the NPY pathway in AcbSh occurs following morphine CPP, and this plasticity plays an important role in modulating morphine reward memory. These findings may enhance our understanding of the role of the NPY system in opioid addiction and indicate a promising target for opioid addiction treatment. • Morphine exposure caused dynamic time- and region-dependent changes in NPY expression. • Blocking Y5 receptor in the AcbSh reduced the maintaining and reinstatement of morphine CPP. • Intra-AcbSh injection of NPY prolonged the duration of extinction period. [ABSTRACT FROM AUTHOR]

Carbon fiber/poly ether ether ketone (Cf/PEEK) composites are a class of high performance, continuous fiber reinforced thermoplastic polymer materials. These composites have the potential to meet demands for self-cleaning or deicing applications in the power supply industry in cold regions. In this study, the effect of graphene on the deicing performance of Cf/PEEK composites through electro-thermal Joule heating was investigated. First, graphene/PEEK composites with varying graphene content of up to 6 wt% were fabricated and characterized. Adding up to 5 wt% graphene was found to improve the electrical conductivity, thermal conductivity, and the crystallinity of PEEK. However, at a graphene content of 6 wt%, the crystallinity and thermal conductivity of the mixture decreased, likely due to agglomeration of graphene. Next, graphene modified Cf/PEEK composites (0 and 5 wt% graphene) with resin volume fractions of 40, 50, and 60 vol% were prepared by hot pressing. Graphene was found to increase the electrical conductivity of the composites by roughly 100%, and to improve the efficiency of converting Joule heating to useful deicing energy by up to 35%. [ABSTRACT FROM AUTHOR]