In this paper, the properties of Hopf bifurcations in a Leslie-Gower Predator-Prey model with delay in predator’s equation have been studied. We have also investigated **optimal** **harvesting** when the **harvesting** is given by a continuous function in this model. Although bifurcations in a population dynamics without delay have been investigated by many researchers, there are few papers on the bifurcations of a population dynamics with delay, which have shown di- rection of global Hopf-bifurcation and **optimal** **harvesting** simultaneously. We have obtained sufficient conditions on the parameters for which the delay-induced system is asymptotically stable around the positive equilibrium for all values of the delay parameter and if the conditions are not satisfied, then there exists a critical value of the delay parameter below which the system is stable and above which the system is unstable. By applying the normal form theory and the center manifold theorem, the explicit formulae which determine the stability and direction of the bifurcating periodic solutions have been determined. Our analytical and simulation results show that when the delay τ passes through the critical value τ 0 0 , the coexisting equilibrium G 0

41 Read more

Abstract - In this paper, we have considered a very general Holling type predator-prey system with selective **harvesting** and where both of the species follow logistic growth. The uniform boundedness of the system has been studied together with the conditions of existence. Also, we have obtained the criteria for local stability of various equilibrium points then considering suitable Lyapunov function, the global stability of the system has been discussed. After that using Pontryagin Maximal Principle, we have studied the **optimal** **harvesting** policy for the system. At the end, the problem has been illustrated through some numerical examples.

A three-species cooperative system with time delays and Lévy jumps is proposed in this paper. Firstly, by comparison method and inequality techniques, we discuss the stability in mean and extinction of species, and the stochastic permanence of this system. Secondly, by applying asymptotic method, we investigate the stability in distribution of solutions. Thirdly, utilizing ergodic method, we obtain the **optimal** **harvesting** policy of this system. Finally, some numerical examples are given to illustrate our main results.

23 Read more

Taking the stochastic eﬀects on growth rate and **harvesting** eﬀort into account, we propose a stochastic delay model of species in two habitats. The main aim of this paper is to investigate **optimal** **harvesting** and dynamics of the stochastic delay model. By using the stochastic analysis theory and diﬀerential inequality technology, we ﬁrstly obtain suﬃcient conditions for persistence in the mean and extinction. Furthermore, the **optimal** **harvesting** eﬀort and the maximum of expectation of sustainable yield (ESY) are gained by using Hessian matrix, the ergodic method, and **optimal** **harvesting** theory of diﬀerential equations. To illustrate the performance of the theoretical results, we present a series of numerical simulations of these cases with respect to diﬀerent noise disturbance coeﬃcients.

17 Read more

in a random environment. Reed (1974) considered a discrete-time optimization model and determined an **optimal** **harvesting** policy in a stochastic growth environment. The selling price was assumed to be …xed, and successive unharvested population levels were assumed to form a Markov chain. The cost of **harvesting** consisted of a …xed one-time set-up cost and a marginal density-dependent harvest cost. An **optimal** **harvesting** policy maximizing the expected net present value of the total pro…t earned over an in…nite time horizon was sought. It was shown that there existed an **optimal** policy of type (S; s) with S < s; where S was a critical threshold for the population. Initiating harvest when the population level was above S resulted in non-negative revenues, however, the revenues could not cover the set-up cost unless the stock-level was well above S: The level s was the smallest population level above S at which the **harvesting** could be initiated pro…tably. Thus the **optimal** policy allowed a harvest in any period if and only if the population level exceeded s; in that case, a harvest down to level S could be made. If the set up cost was zero then **harvesting** could be initiated pro…tably once the population level exceeded S; and therefore S was equal to s.

209 Read more

Abstract. In this paper, we investigate the **optimal** **harvesting** problem for a class of nonlinear population system with fertility and mortality depending on the population size. Fixed point theory is used to obtain the existence and uniqueness of nonnegative solution in terms of the controls. Optimality conditions are derived by means of normal cone technique. The existence of the **optimal** control is carefully verified via Ekeland’s variation principle, some results in references are extended.

15 Read more

Therefore, the prey species can be maintained at an appropriate level. As per observational information of Lake Kasumigaura in Japan, Kitabatake [11] built up a dynamic model for fishery assets with a prey–predator system in a two-patch environment. He examined the possibilities of the existence of bionomic equilibrium and an **optimal** **harvesting** policy is given by Pontryagin’s maximum principle. Srinivasu and Gayatri [12] observed that the reserve capacity has a vital part in guaranteeing eitherpresence of predators or their eradication. Kar and Matsuda [13] established the significance of marine protected areas (MPAs), from both economic and biological perspective. Rui Zhang [14] has demonstrated that in the absence or within the sight of predators, the ﬁshing populations may be remaining at an suitable equilibrium level. Yunfei et al. [15] investigated that marine reserves ensured the sustainability of the system. Aquatic reserves secure both the species inside the reserve area as well as increase fish abundance in adjoining areas. An appropriate equilibrium level of prey population is always maintained irrespective of presence or absence of predators in the unreserved zone. Amit Sharma and Bhanu Gupta [16] studied the dynamics of fishery resource with reserve area in the presence of bird predator. In this work they have given criteria for finding the biological and bionomic equilibrium points of the system.Optimal **harvesting** policy has also established using Pontryagin’s maximum principle.

10 Read more

We study the problem of **optimal** **harvesting** of a marine species in a bounded domain, with the aim of minimizing harm to the species, under the general assumption that the fishing boats have di ff erent capacities. This is a generalization of a result of Kurata and Shi, in which the boats were assumed to have the same maximum **harvesting** capacity. For this generalization, we need a completely di ff erent approach. As such, we use the theory of rearrangements of functions. We prove existence of solutions, and obtain an optimality condition which indicates that the more aggressive **harvesting** must be pushed towards the boundary of the domain. Furthermore, we prove that radial and Steiner symmetries of the domain are preserved by the solutions. We will also devise an algorithm for numerical solution of the problem, and present the results of some numerical experiments.

18 Read more

A practical time-scale for sustainability for natural resource management broadly equates to 80–100 years. After that time, it would be difficult for people to imagine what society might be like. Even making predictions of what constitutes sustainability within that time period will be difficult because of natural changes beyond human control and changes to the way humans use natural resources. These issues become more focused when considering different forms of property rights, including those involving exploitation for commercial gain, as in fisheries. In this case, a minimum expectation is that those exploiting the resources would seek commercial returns on capital invested in acquiring access, and in **harvesting** and developing the resources. Open access and some forms of common property ownership result in overexploitation and collapse of resources, rather than in sustainable biological and social outcomes. This is not sufficient reason to argue that renewable natural resources should be maintained in government ownership and commercial exploitation prohibited. In reality, natural resources treated in this manner assume no value to the community, other than their intrinsic ecological and existence values. These resources are even more likely to be degraded or lost.

**Harvesting** in the predator-prey system is the killing of predator and prey species for the purpose of human consumption or trade. The problems of predator-prey systems with **harvesting** have been explored by many researchers, however most of them have put attention on the **optimal** **harvesting** guided entirely by economic profits from **harvesting** [7] [8]. In fact, **harvesting** of species should be done by considering both economic and biological values of the population [9]. Recently, it has been observed that, the biological species of predator-prey system is harvested and sold for the purpose of making economic profit which slowly decreases the species and finally the ecosystem collapses [10].

24 Read more

Abstract. In this paper, we propose a predator-prey model with **harvesting** and reserved area for prey with the presence of competition and toxicity with two effort functions. First, we prove the boundedness of the solutions. Then, the existence is studied, as well as the local and global stability of the equilibria. Lyapunov proved this last with certain conditions. The **optimal** **harvesting** policy is discussed using the Maximum Principle of Pantryagin. Finally, we ensure our results by numerical simulations.

25 Read more

Finally, we generalise a result from one of the stochastic models in [Smi78], where the equivalent to our yield function has a specific simple form. We show that, when the yield function is weakly convex, the **optimal** control is bang-bang. However, if the yield function is strictly concave, then the **optimal** **harvesting** strategy has to be continuous, in contrast to the bang-bang type **optimal** strategy we find for a linear yield function. This generaliza- tion is useful for economic welfare analysis (a more general form of cost-benefit analysis), which typically relies on a concave utility function, equivalent to the concave yield function herein. In economic models, concavity is assumed to model risk aversion (see [MCWG95, Proposition 6.C.1] for justification), and for the convenience of interior solutions to max- imisation problems. Concave utility leads to a trade-off between risk and returns in asset choice [Mer71], so the connection between yield concavity and strategy continuity mentioned

33 Read more

To obtain the results in this paper, we used the well-known quasi-Newton method (see, e.g., [10–12]) to ﬁnd the **optimal** **harvesting** policies from the model given in Eq. (4)– (7) for the two types of sugarcane for the four regions of Thailand for the crop years 2012/13, 2013/14, and 2014/15. The numerical results were obtained using the con- strained optimization function fmincon in Matlab with the “active-set” algorithm se- lected. For these solutions, we used the price and cost data supplied by the OCSB that has been discussed in the Mathematical Models section. Also, as stated earlier after Eq. (4)–(7), we assumed that r = 0, i.e., no growth of sugarcane during the cutting sea- son.

15 Read more

91 Thus, earlier research suggests that further investigation should be done on reducing the skin damage and separation at the time of harvest. Development of a sweetpotato vine puller- chopper **harvesting** aid to separate the main stem from the individual roots below the soil has been an important step towards reducing sweetpotato skinning. Quantifying the effect of the vine-root separation by the **harvesting** aid on the skin strength of the sweetpotato roots prior to harvest is a key objective of this study. The hypothesis is that the vine-root separation initiates the skin set process by cutting the nutrient supply and water intake to the sweetpotatoes and as a reaction to the change, the root skin would toughen. This study involving the quantification of skin strength due to vine-root separation by the vine puller-chopper machine should provide the sweetpotato growers with information on skin toughness during **harvesting**. Additionally, this study should also benefit the sweetpotato equipment manufacturers to design the appropriate **harvesting** and post-harvest machinery to minimize skin damage. At a larger scale, this study should enhance technology development in the sweetpotato industry and help in mechanizing the **harvesting** process.

165 Read more

Single centre studies reported results supporting the NT hypothesis [11]. This is the first multi-centre RCT to assess the No Touch SVG compared to the conven- tional SVG **harvesting** technique for 1 year outcomes. Collaborating centres received training by two of the in- vestigators familiar with the technique (DDS, SEF). Study SVG occlusion, and study SVG stenosis or occlu- sion, were lower, but not significantly different, in the NT SVGs in the current study. When all SVGs were considered, the on-treatment analysis of graft stenosis or occlusion was significantly reduced in the NT SVGs sug- gesting biological superiority. The aggregated data does show a clinically important reduction in graft occlusion (Fig. 4a) and graft stenosis or occlusion (Fig. 4b). The point estimates from this current study are also consist- ent with the earlier single centre studies without hetero- geneity. Furthermore and importantly, graft occlusion of the NT veins to non-LAD targets and internal mammary grafts to the LAD at 16 years in the original Swedish study was not statistically different [11].

10 Read more

Abstract: The abundant mechanical vibration energy in bridge road environment can be converted into electric energy by using the piezoelectric energy harvest technology, which could be an efficient way to provide energy required by the wireless sensor network in the bridge condition monitoring system. An autonomous energy **harvesting** system has been designed based on cantilever beams for sensing and acquiring the bridge vibration energy. After the analysis of the dynamic properties of the piezoelectric cantilever beam in the energy conversion, three kinds of interface circuits were compared through simulation and experimental results. It was shown that the VD interface circuit has less power loss. Furthermore, the proposed closed loop control method based on the VD circuit was simple, adaptive, and self-powered, which is suitable for the road energy **harvesting** application. Finally, the energy **harvesting** system based on VD circuit was realized with harvested power of around 0.8mW.

23 Read more

In fact, the former papers [4–7] have only considered point-to-point wireless communications without using CR technology. Recently, some researches have focused on the combination of EH technology and CRN, and dif- ferent OPAs are discussed in [8–14]. The OPA for EH CRN is studied in [8], the authors consider the problem of system throughput maximization over a finite hori- zon rather than at a certain time slot, and they adopt a rate loss constraint to protect the transmission of pri- mary user (PU). The access strategy for hybrid underlay- overlay CR networks with EH is analyzed in [9]. The partially observable Markov decision process (POMDP) framework is proposed to determine the action of SU; meanwhile, energy threshold is used to determine the transmission mode of SU. In [10], considering an EH- CR system, a power allocation policy with peak power constraints is proposed, and the target throughput max- imization problem is solved by recursion machinery and geometric water-filling algorithm. A novel saving-sensing transmitting (SST) frame structure for EH CRNs is pro- posed in [11], where the authors aim to maximize the energy utilization efficiency of SU by jointly optimizing the save ratio and transmission power under both the energy causality constraint and the minimum throughput constraint. And the SST can make full use of residual bat- tery energy as well as ensure enough time for spectrum sensing and data transmission. A generalized multislot spectrum sensing paradigm and two types of fusion rules (data fusion and decision fusion) are proposed in [12]. The authors focus on the trade-off of “**harvesting**-sensing- throughput” and joint optimization for save ratio, sensing duration, and sensing threshold as well as fusion rule to maximize the expected achievable throughput of SU while keeping the protection to PU. A POMDP is proposed in [13] to trade off energy consumption and throughput gain in hybrid CRN, where SU dynamically determines its operation mode for each time slot ( e.g., to be idle or to transmit), sensing time, and access mode. In [14], for an overlay EH CRN, the authors aim to find an **optimal** sensing time to maximize throughput of SU and harvested RF energy. Most of the existing works only investigate OPA problem in CR system with single user, which is not pratical for real communication systems.

10 Read more

Japan's strawberry-**harvesting** robot images the berries before deciding if they're ripe. Strawberry fields will forever be changed by robots that can automatically identify and pick ripe berries, according to Japanese researchers. Developed by the minds at an organization aptly abbreviated IAM-BRAIN (that's the Institute of Agricultural Machinery's Bio-oriented Technology Research Advancement Institution), the machines can harvest more than 60 percent of a strawberry crop. The robot targets berries that are at least 80 percent red. Even though each machine takes nine seconds to pick a strawberry, they can cut **harvesting** time from 500 hours to 300 hours for a 1,000-square-meter field (about a quarter-acre), BRAIN's Shigehiko Hayashi explains in the video below.

In this study, the design of optimized energy **harvesting** device is constrained to materials that are commonly available and other experimental limitations, such as unavailability of the substrate with uniform residual strain distribution, the machining technologies and laminating MsM layers on the substrate by hand. Moreover, the design was limited to use the low coupling coefficient MsM material, cast Metglas 2605SA1 and stainless steel substrate. It is quite easy to cut both MsM and steel material to any size in length and width but their thickness is constrained by what the manufacturer products. The thickness of the stainless steel substrate and Metglas 2605SA1 (cast) is 150 µm and 22.86 µm, respectively. Moreover, more non-uniform residual strain was induced to the cantilever beam when cutting the device. When bonding two MsM layers onto the stainless steel using 3M Acrylic DP810 Epoxy, imperfect bonding existed between the layers. It in turn increased the mechanical damping. The resulting thickness of the device is 0.21 mm.

179 Read more

There are two types of **harvesting**, one of them is manual **harvesting** and other one is mechanized types of **harvesting**. The time required in manual **harvesting** is more than **harvesting** using machines, it takes approximately 15 to 16 labours to harvest one acre of land in 3 days. The labours being paid 500 to 550 Rupees. Per ton of harvest so total cost of **harvesting** of one acre of land comes around 30,000 to 35,000Rupees. In mechanization now by using large scale **harvesting** machine takes 6 to 7 hours for **harvesting** of 60 to 70 tons while labour cost is around 4,000