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The paper presents a two-species prey-predator scenario in which both exhibit swarm behaviour. As a result, due to this co-operative behaviour after harvesting an intra-specific competition occurs between predators. Our research demonstrates that the system's stability is significantly influenced by their inter-dependent competitiveness and joint harvesting effort. We start out by talking about the model's Positivity and Boundedness. The equillibria are analysed and displayed. A Hopf-Bifurcation criterion is discovered. The next step is to do numerical simulations to help explain some of the mathematical findings. We will better grasp the dynamics of predator-prey interaction in natural environments with the help of this model. [ABSTRACT FROM AUTHOR]

This paper establishes a prey–predator model with a Holling type IV functional response and proportional harvesting in prey species and nonlinear harvesting in predator species. We provide a completely local and global bifurcation analysis of the model to characterize some meaningful results that may emerge from the interaction of biological resources. The proposed model exhibits various complex behaviors involving heteroclinic and homoclinic orbits, and we prove analytically that it also undergoes transcritical, Hopf, and Bogdanov–Takens bifurcations in the prey–predator plane. Moreover, the system is unfolded to compute the bifurcation curves, highlighting the critical dynamics by perturbing two bifurcation parameters near the cusp. Furthermore, from the economic point of view, the bionomic equilibrium of the system is studied, and optimal harvesting policy is derived using the Pontryagin’s maximum principle. Numerical simulations are presented to verify our analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we delve into a predator–prey model incorporating a fear effect in prey reproduction, influenced by both delay and harvesting. The model accounts for delayed fear dynamics to capture more realistic dynamics. Initially, our focus lays on the nondelayed model, examining each biologically plausible equilibrium points and assessing their stability concerning the parameters of the model. Next, detailed mathematical results are provided, encompassing the asymptotic stability of all equilibria, Hopf bifurcation, and the direction and stability of bifurcated periodic solutions. Also, the stability analysis of the Hopf-bifurcating periodic solution is confirmed through the computation of first Lyapunov coefficient. Furthermore, we observed that the nondelayed system experiences Bogdanov–Takens bifurcation in a two-parameter space. Subsequently, we analyzed the corresponding delayed system, establishing the existence of a stable limit cycle through Hopf bifurcation concerning the delay parameter. Additionally, the inclusion of delay can prompt critical dynamics within the system, resulting in period-doubling routes toward chaotic oscillations. To validate our analytical findings, we conducted comprehensive and meticulous numerical simulations. The findings of the numerical simulations suggest that the impact of fear can be used as a measure of chaos control. [ABSTRACT FROM AUTHOR]

Recently, Christian Cortés García proposed and studied a continuous modified Leslie–Gower model with harvesting and alternative food for predator and Holling-II functional response, and proved that the model undergoes transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation. In this paper, we dedicate ourselves to investigating the bifurcation problems of the discrete version of the model by using the Center Manifold Theorem and bifurcation theory, and obtain sufficient conditions for the occurrences of the transcritical bifurcation and Neimark–Sacker bifurcation, and the stability of the closed orbits bifurcated. Our numerical simulations not only illustrate corresponding theoretical results, but also reveal new dynamic chaos occurring, which is an essential difference between the continuous system and its corresponding discrete version. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the dynamical behaviors of a piecewise smooth predator–prey model with predator harvesting. We consider a harvesting strategy that allows constant catches if the population size is above a certain threshold value (to obtain predictable yield) and no catches if the population size is below the threshold (to protect the population). It is shown that boundary equilibrium bifurcation and sliding–grazing bifurcation can happen as the threshold value varies. We provide analytical analysis to prove the existence of sliding limit cycles and sliding homoclinic cycles, the coexistence of them with standard limit cycles. Some numerical simulations are given to demonstrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a predator–prey model with Cosner type functional response and combined harvesting. First, we explore the existence and stability of the equilibria. Then using the center manifold theorem and normal form theory, we investigate codimension one and codimension two bifurcations of the model. The analysis shows that the system has a variety of bifurcation phenomena including transcritical bifurcation, saddle‐node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation and homoclinic bifurcation. Our findings indicate that the dynamics with harvesting are significantly richer than the system without harvesting. Finally, numerical simulations are provided to support the analytical results. [ABSTRACT FROM AUTHOR]

In this paper, some complicate dynamical behaviors are formulated for a discrete predator–prey model with group defense and nonlinear harvesting in prey. After considering the existence and stability for all of its nonnegative fixed points, our main work is to present those conditions for the occurrences of transcritical bifurcation, saddle-node bifurcation and Neimark–Sacker bifurcation, respectively. Numerical simulations not only verify the theoretical results for saddle-node bifurcation and Neimark–Sacker bifurcation but also display more interesting dynamical properties of the model. [ABSTRACT FROM AUTHOR]

A diffusive predator–prey system with the network connection and harvesting policy is investigated in the present paper. The global existence and boundedness of the positive solutions to the parabolic equations are analyzed. Hereafter, a priori estimates and non‐existence of the non‐constant steady states are investigated for the corresponding elliptic equation. Next, we focus on the network connect model. The stability of the positive equilibrium, the Hopf bifurcation, and the Turing instability of networked system are explored. By using the multiple time scale (MTS), the direction of the Hopf bifurcation is determined. It is found that the networked system may admit a supercritical or subcritical Hopf bifurcation. For the Turing instability, the positive equilibrium will change its stability from an unstable state to a stable one with the change of the connecting probability. That is not the case in the model without network structure. Theoretical results also show that the model can create rich dynamical behaviors and numerical simulations well verify the validity of the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, a Beddington–DeAngelis prey–predator model with fear effect, refuge and harvesting is investigated. First, the positivity of solutions and boundedness of system are given. Then, the existence and local stability of equilibria of such system are obtained. Next, not only different codimension-one bifurcations, such as saddle-node bifurcation, transcritical bifurcation and Hopf bifurcation take place, but also Bogdanov–Takens bifurcation of codimension-two occurs as predicted by the center manifold theorem and bifurcation theory. Finally, some numerical simulations are carried out to confirm our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a generalized population model with delays and harvesting term is studied, which includes some well-known models, such as Gilpin–Ayala competitive model and Logarithmic model. By a suitable Lyapunov function and the Banach fixed point theorem, we obtain the existence and uniqueness of globally attractive pseudo almost periodic solution of the model and prove its permanence. Some examples and numerical simulations are given to illustrate the feasibility and usefulness of the model and results. [ABSTRACT FROM AUTHOR]

This paper developed six cable logging incident scenarios that were modeled in a simulated environment, and conducted a pilot study in the Pacific Northwest to assess the potential for collecting worker risk assessment data. All the subjects in the pilot study reported that they understood the simulated incidents, and they were able to move around in the simulation to see what they needed. When reporting management requiring conditions (MRC) before performing the simulated task, the subjects consistently identified the first main MRC; however, there was variation in reporting the second main MRC. The results from the pilot study indicate that the simulations effectively modeled the spatial aspects of the incidents; however, the simulations lacked avatars to represent people in the simulations and this may have limited the ability to include cognitive aspects such as communication. Variation in the severity assigned by the subjects to the MRC, and to the unexpected events, revealed important differences in risk sensitivity between the subjects, and the importance of experiential learning in a safe environment when considering energized systems. [ABSTRACT FROM AUTHOR]

Models of plankton-fish based ecosystems with delay have received a great deal of attention in the last few decades. This paper deals with a plankton-fish based ecosystem involving phytoplankton. zooplankton and planktivorous fish. Initial analysis of various possible equilibrium points and their steady states behavior demonstrates that mortality rate and harvesting rate of planktivorous fish and intrinsic growth rate of zooplankton play key roles to stabilize the system. Further, conditions for global stability and direction of Hopfrbifurcation is also discussed. A path of optimal harvesting policy is derived by introducing the Pontryagins maximum principle. Further. a discrete time delay term due to gestation in the functional response is introduced in the growth equation of planktivorous fish. In addition. estimate for the length of time delay to preserve the stability of the model system is exploded. Existence of Hopf bifureating small amplitude periodic solutions is derived by considering time delay as a biturcation parameter. Computer simulations are implemented to help the analytical results. [ABSTRACT FROM AUTHOR]

Filippov systems have found applications in various fields. This paper mainly studies five Lotka–Volterra models of Filippov type, including a competitive system with linear interaction between two species, a competitive system with Holling type II or type III functional response and a symbiosis system with Holling type II or type III functional response. We investigate the stability of all equilibria and the boundary equilibrium bifurcations of these systems, either a persistence bifurcation or a nonsmooth fold bifurcation. We present the numerical simulation results for each case. Consequently, based on both theory and simulation, we analyze the ecological aspects under the intervention of harvesting at different prescribed thresholds. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamical response and vibrational resonance (VR) of a piecewise electromechanically coupled tri-stable energy harvester (TEH), which is driven by dual-frequency harmonic excitations. To achieve a stable DC output, the TEH is interfaced with a standard rectifier circuit. Using the harmonic balance method combined with the separation of fast and slow variables, a steady-state response together with the analytical expressions of displacement and harvested power is derived. The multi-solution feature in the amplitude–frequency response is observed and can improve the harvesting performance of the TEH under a low-frequency environment. There is an optimal time constant ratio and electromechanical coupled coefficient to maximize the harvested DC power. Meanwhile, the VR phenomenon of the TEH is explored through the response amplitude of the low-frequency input signal, which implies that an appropriate combination can induce the occurrence of VR and improve the rectified voltage. Similarly, the nonlinear stiffness coefficients can be adjusted by changing the magnet distance to induce the appearance of VR. The theoretical solutions are well supported by numerical simulation and experimental verification. Specifically, the theoretical analysis and experimental evidence illustrate that the harvested power under the VR effect is much higher than that without VR. [ABSTRACT FROM AUTHOR]

A discrete cooperative model incorporating harvesting that takes the form is proposed and studied in this paper. By using the iterative method and the comparison principle of difference equations, a set of sufficient conditions which ensure the global attractivity of the interior equilibrium of the system is obtained. Numeric simulations show the feasibility of the main result. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated global dynamics of a two-species food chain model with the Holling type III functional response that includes linear harvesting for the prey and nonlinear harvesting for the predator. The long-time continued existence of both species is discussed using uniform persistence theory. Stability of various equilibrium points is described in terms of model parameters. The local asymptotic stability of non-hyperbolic equilibrium points is determined with the help of center manifold theorem. Global behavior of solutions of the model system when both species are present is determined by considering the global properties of the coexistence equilibrium. Here, we have taken a comprehensive view by considering different bifurcations of co-dimension one and two and have discussed the importance of various model parameters on the system dynamics. The model system shows much more complex and realistic behavior compared to a model system without any harvesting, with constant harvesting or linear-yield harvesting of either or both of the species. Numerical simulations have been conducted to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, an eco-economic model with harvesting on biological population is established, which takes the form of a differential-algebra system. The impact of the economic profit from harvesting upon the dynamics of the model is studied. By using a suitable parameterization for the differential-algebra system, we derive an equivalent parameterized system which gives the stability results for the positive equilibrium point of our model. Moreover, based on the parameterized system as well as the approaches of normal form and formal series, the conditions on the Hopf bifurcation and the stability of center are obtained. Several numerical simulations for demonstrating the theoretical results are also presented. Lastly, according to the dynamical analysis, we provide a threshold value for the economic profit, which can maintain the sustainable development of our eco-economic system. [ABSTRACT FROM AUTHOR]

This paper proposes and investigates a nonselective harvesting Lotka-Volterra predator-prey system that incorporates population closure and the fear effect of the prey. The boundary equilibrium and positive equilibrium are studied in terms of their local and global stability characteristics. Our research indicates that the proportion of commodities designated for harvesting has a significant impact on the dynamic behavior of the system. Meanwhile, dynamic behavior of the system is not affected by the fear effect of the prey species. To demonstrate the viability of the key findings, numerical simulations are performed. [ABSTRACT FROM AUTHOR]

A diffusive phytoplankton–zooplankton model with nonlinear harvesting is considered in this paper. Firstly, using the harvesting as the parameter, we get the existence and stability of the positive steady state, and also investigate the existence of spatially homogeneous and inhomogeneous periodic solutions. Then, by applying the normal form theory and center manifold theorem, we give the stability and direction of Hopf bifurcation from the positive steady state. In addition, we also prove the existence of the Bogdanov–Takens bifurcation. These results reveal that the harvesting and diffusion really affect the spatiotemporal complexity of the system. Finally, numerical simulations are also given to support our theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, the particle filtering problem is investigated for a class of nonlinear/non-Gaussian systems with energy harvesting sensors subject to randomly occurring sensor saturations (ROSSs). The random occurrences of the sensor saturations are characterized by a series of Bernoulli distributed stochastic variables with known probability distributions. The energy harvesting sensor transmits its measurement output to the remote filter only when the current energy level is sufficient, where the transmission probability of the measurement is recursively calculated by using the probability distribution of the sensor energy level. The effects of the ROSSs and the possible measurement losses induced by insufficient energies are fully considered in the design of filtering scheme, and an explicit expression of the likelihood function is derived. Finally, the numerical simulation examples (including a benchmark example for nonlinear filtering and the applications in moving target tracking problem) are provided to demonstrate the feasibility and effectiveness of the proposed particle filtering algorithm. [ABSTRACT FROM AUTHOR]

The paper is concerned with the optimal harvesting of a marine park, which is described by a parabolic heat equation with Neumann boundary conditions and a nonlinear source term. We consider a cost functional, which is linear with respect to the control; hence the optimal solution can belong to the class of measure-valued control strategies. For each control function, we prove existence and stability estimates for solutions of the parabolic equation. Moreover, we prove the existence of an optimal solution. Finally, some numerical simulations conclude the paper. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics. [ABSTRACT FROM AUTHOR]

In this paper, a Holling-Tanner predator-prey model with ratio-dependent functional response and non-linear prey harvesting is analyzed. The mathematical analysis of the model includes existence, uniqueness and boundedness of positive solutions. It also includes the permanence, local stability and bifurcation analysis of the model. The ratio-dependent model always has complex dynamics in the vicinity of the origin; the dynamical behaviors of the system in the vicinity of the origin have been studied by means of blow up transformation. The parametric conditions under which bionomic equilibrium point exist have been derived. Further, an optimal harvesting policy has been discussed by using Pontryagin maximum principle. The numerical simulations have been presented in support of the analytical findings. [ABSTRACT FROM AUTHOR]

In this paper, a fractional-order predator–prey mathematical model has been developed considering Holling type II functional response. Here, we have investigated the interaction dynamics of prey, middle predator and top predator. We assume that the middle predator consumes only the prey, and the top predator consumes only the middle predator. Here, the logistic growth of prey has been considered. Then, different possible equilibrium points of our proposed system are determined. The stability of our proposed system is investigated around the equilibrium points. Then, some numerical simulations results are presented for better understanding the dynamics of our proposed model. It is found that the fractional-order derivative can improve the stability of our proposed system. [ABSTRACT FROM AUTHOR]

A stage-structured prey–predator model with prey refuge is assumed, where predators have two stages as immature and mature. We consider here the harvesting on prey only and analyze the model using Beddington-DeAngelis functional response. Local stability as well as global stability at an interior equilibrium point are investigated in the proposed model. We choose different types of bifurcation like Hopf bifurcation, saddle-node bifurcation, and transcritical bifurcation in the formulated model. Moreover, in this paper, we check the optimality of the harvesting function with the help of optimal control. We provide the numerical simulation of the proposed model for the confirmation of analytical results. [ABSTRACT FROM AUTHOR]

Sunflower (Helianthus annuus L.) is one of the four major oil crops in the world and has high economic value. However, the lack of discrete element method (DEM) models and parameters for sunflower seeds hinders the application of DEM for computer simulation in the key working processes of sunflower seed sowing and harvesting. The present study was conducted on two varieties of sunflower, and the DEM model of sunflower seeds was established by using 3D scanning technology based on the distribution of triaxial dimensions and volumes of the geometric model of sunflower seeds. Similarly, the physical characteristics parameters of sunflower seeds were determined by physical tests and the simulation parameters were screened for significance based on the Plackett-Burman test. Our results show that the coefficient of static friction between sunflower seeds and the coefficient of rolling friction have significant effects on the repose angle of the simulation test. Furthermore, the optimal range of the significance parameters was further determined by the steepest climb test, and the second-order regression model of the significance parameters and the repose angle was obtained according to the Box-Behnken design test and Response Surface Methodology (RSM), with the repose angle measured by the physical test as the optimized target value to obtain the optimal parameter combination. Finally, a two-sample t-test for the repose angle of the physical test and the repose angle of the simulation test yielded P > 0.05. Our results confirms that the repose angle obtained from simulation is not significantly different from the physical test value, and the relative errors between the repose angle of the simulation test and the physical test are 1.43% and 0.40%, respectively, for the optimal combination of parameters. Based on these results it can be concluded that the optimal parameters obtained from the calibration can be used for DEM simulation experiments related to the sunflower seed sowing and harvesting process. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an aquatic ecological model of microcystis aeruginosa-filter feeding fish and predatory fish model with aggregation effect of microcystis aeruginosa. Fear effect of predatory fish on filter feeding fish and harvesting effect of big fish is considered. Mathematical analysis includes two parts. The first is theoretical part, which includes proving the positive and constraining solutions of the model. Also finding equilibrium points and studying their local stability is included in this part. In addition, analyzing the local bifurcation of equilibrium points and indicating the type of bifurcation is discussed here. On the other hand, the second part contains the numerical simulation of all the theoretical results, where we compare the numerical values of the conditions obtained in the theoretical part. [ABSTRACT FROM AUTHOR]

This paper is concerned with a single-species model with nonlinear harvesting rate and feedback control on time scales, which modified from Ref. [11]. Based on the theory of calculus on time scales, by applying the methods used in Ref. [11], but improved, sufficient conditions which guarantee the permanence and the existence of a unique globally attractive positive almost periodic solution of the system are obtained. Finally, numerical simulations are presented to illustrate the feasibility and effectiveness of the results. The results in this paper improved and generalized the results derived in [11]. [ABSTRACT FROM AUTHOR]

The present paper deals with a prey–predator model with prey refuge in proportion to both species, and the independent harvesting of each species. Our study shows that using refuge as control, it can break the limit cycle of the system and reach the required state of equilibrium level. We have established the optimal harvesting policy. The boundedness, feasibility of interior equilibria and bionomic equilibrium have been determined. The main observation is that the coefficient of refuge plays an important role in regulating the dynamics of the present system. Moreover, the variation of the coefficient of refuge changes the system from stable to unstable and vice-versa. Some numerical illustrations are given in order to support our analytical and theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a plankton system consisting of two plankton species one is toxin producing plankton, another is non-toxin producing plankton and zooplankton population which depends on both the phytoplankton species. We investigate the boundedness and stability criteria of the system and existence conditions of all possible equilibria. It is observed that if the inhibitory effects of the toxin producing phytoplankton crosses a certain critical value, the system enters into Hopf bifurcation. It is observed that the carrying capacity of non toxin phytoplankton population plays an important role to change steady state to oscillatory behavior of the system. Further, we have studied a path of optimal harvesting policy by introducing the Pontryagin's maximum principle. Computer simulations illustrate the results. [ABSTRACT FROM AUTHOR]

• 3-degrees of freedom (dof) linear multi-arm robotic fruit harvester models were used to harvest the fruits on high density pear and peach trees. • Pick cycle times of multi-arm robotic fruit harvesters (PCTM's) were low when the arms were arranged in height split configuration compared to length split, height split matrix, and length split matrix configurations. • Harvesting the tree sides separately resulted in lower PCTM's than harvesting both sides of the trees at once with a harvester having the same number of arms while traversing in an orchard row. • Lower pick cycle times (PCT's) that could compete with human PCT's can be achieved using linear multi-arm harvesters. In some cases, it has been shown that fruits on trees with SNAP (Simple, Narrow, Accessible, and Productive) architectures are reachable by robot arms using three linear degrees of freedom; hence, high fruit-picking efficiencies can be achieved with simpler arms. This paper uses digitized fruit position data to compute the fruit pick cycle times (PCT) of robotic fruit harvesters with multiple arms arranged in grid configurations, i.e., operating in disjoint rectangular work cells independently of each other. The effects of the robot joints' maximum linear acceleration and maximum linear velocity on PCTs were studied. As V max increased, the PCT followed a negative exponent power law (diminishing return) for any given A max. Similarly, for a constant V max , the improvement of PCT as A max increased slowed down at higher acceleration values. Also, the PCTs were computed when each arm work cell was designed based on equal fruit load or equal size criteria, using four workspace partitioning schemes (height split, length split, height split matrix, and length split matrix). Equal fruit-load configurations resulted in load balancing and exhibited lower PCTs; the height-split configuration was the best among the four different partitioning schemes, possibly because it compensated better for the fruit distribution's non-uniformity along the trees' height. Finally, the PCTs were computed while harvesting one side of an orchard row or both sides concurrently. Harvesting sides separately resulted in lower PCTs (greater speed) due to non-uniform fruit distributions on the different sides of trees. The insights gained in this paper can inform the design of harvesting robots utilizing arrays of 3-dof linear arms. [ABSTRACT FROM AUTHOR]

The predator–prey model is fundamentally important to study the growth law of the population in nature. In this paper, we propose a diffusive predator–prey model, in which we also consider time delay in the gestation time of predator and Michaelis–Menten type predator harvesting. By analyzing the distribution of eigenvalues, we investigate the stability of the coexisting equilibrium and the existence of Hopf bifurcation using time delay as bifurcation parameter. We analyze the property of Hopf bifurcation, and give an explicit formula for determining the direction and the stability of Hopf bifurcation. Finally, some numerical simulations are given to support our results. [ABSTRACT FROM AUTHOR]

This paper presents a prey-predator harvesting model with time delay for bifurcation analysis. We consider the parameters of the proposed model with imprecise data as form of interval in nature, due to the lack of precise numerical information of the biological parameters such as prey population growth rate and predator population decay rate. The interaction between prey and predator is assumed to be governed by a Holling type II functional response and discrete type gestation delay of the predator for consumption of the prey under impreciseness of the biological parameters. Parametric functional form of interval number with two parameters is introduced. This study reveals that not only delay and harvesting effort play a significant role on the stability on the system but also interval parameters play a crucial role on the stability of the system. Computer simulations of numerical examples are given to explain our proposed imprecise model. We also address critically the biological implications of our analytical findings with proper numerical example. [ABSTRACT FROM AUTHOR]

In this paper we consider a harvesting model of predator-prey fishery in which the prey is directly infected by some external toxic substances. The toxic infection is indirectly transmitted to the predator during the feeding process. The model is a modified version from the classic Lotka-Volterra predator-prey model. The stability and bifurcation analyses are addressed. Numerical simulations of the model are performed and bifurcation diagrams are studied to investigate the dynamical behaviours between the predator and the prey. The effects of toxicity and harvesting on the stability of steady states found in the model are discussed. [ABSTRACT FROM AUTHOR]

In this paper, nonlinear mathematical models have been proposed for comparative study of dynamics of CO2 with respect to vegetation biomass considering different growths of vegetation biomass, such as logistic, regrowth and regrowth with delay. Here we have considered harvesting of vegetation biomass due to external factors. Conditions for boundedness, local and global stability of equilibrium points and persistence has been derived for the models. Numerical simulations has been carried out to support analytical results and analyse bifurcation with respect to parameters (growth rates, catchability coefficient and depletion rate of CO2 due to vegetation biomass). Model analysis reveals that, as compared to logistic growth, regrowth allows us a large span for harvesting in which system remains stable. Model analysis also shows that the model in which we have considered regrowth, density of vegetation biomass and concentration of CO2 bifurcate negligibly with respect to different parameters as compared to logistic growth. Since often there exist a time lag for regrowth so we have also calculated critical value of lag after which system get unstabilized. [ABSTRACT FROM AUTHOR]

In this paper, we propose a mathematical model for a single species fish stock with a three-stage structure: Juveniles, small adults, and large adults with two harvesting strategies for mature classes, maturity, and size selectivities. The purpose of the work is to investigate the dynamical behavior of the model and discuss the effect of harvesting. We identify the adult reproduction number RA for the model; obtain the local and global stability of the trivial equilibrium when RA < 1; and discuss the population persistence and existence of a unique positive equilibrium when RA > 1. Numerical simulations are provided to investigate the inuence of harvesting functions, discuss the optimal harvesting rates, and explore the effect of periodic coefficients on the dynamical system. [ABSTRACT FROM AUTHOR]

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In this paper we propose a periodic impulsive delay two-species competitive system in which two species have toxic inhibitory effects on each other. It is assumed that the system is impulsively controlled by means of harvesting and stocking controls. By using the theory of impulsive differential equation and analysis techniques, a set of sufficient conditions are derived for the permanence and partial extinction of the system. It turns out that the impulsive controls play a crucial role in shaping the above dynamics of the system. Numerical simulations are presented to substantiate the analytical results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

When it comes to harvesting operations, precision agriculture needs to consider both combine harvester technology and the precise execution of the process to eliminate harvest losses and minimize out-of-work time. This work aims to propose a complete control framework defined by a two-layer-based algorithm and a simulation environment suitable for quantitative harvest loss, time, and consumption analyses. In detail, the path-planning layer shows suitable harvesting techniques considering field boundaries and irregularities, while the path-tracking layer presents a vision-guided Stanley Lateral Controller. In order to validate the developed control framework, challenging driving scenarios were created using IPG-CarMaker software to emulate wheat harvesting operations. Results showed the effectiveness of the designed controller to follow the reference trajectory under regular field conditions with zero harvest waste and minimum out-of-work time. Whereas, in presence of harsh road irregularities, the reference trajectory should be re-planned by either selecting an alternative harvesting method or overlapping the harvester header by some distance to avoid missing crops. Quantitative and qualitative comparisons between the two harvesting techniques as well as a relationship between the level of irregularities and the required overlap will be presented. Eventually, a Driver-in-the-loop (DIL) framework is proposed as a methodology to compare human and autonomous driving. [ABSTRACT FROM AUTHOR]

This paper deals with a prey-predator model in which both the species are infected by some toxicants which are released by some other species or source with fuzzy biological parameters. The application of fuzzy differential equation in the modeling of prey-predator populations with the effect of toxicants is presented. The dynamical behavior and harvesting of the fuzzy exploited system are studied by using the utility function method. Sufficient conditions for the local stability of the positive equilibrium are obtained by analyzing the characteristic equation. Furthermore, the possibility of the existence of bionomic equilibrium is studied under imprecise biological parameters. The study of the presence of toxic substance and harvesting in the modeling system can have significant impact on the existence of both the species, which is in line with reality. Numerical simulation results are presented to validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper an eco-epidemiological model incorporating a prey refuge and prey harvesting with disease in the prey-population is considered. Predators are assumed to consume both the susceptible and infected prey at different rates. The positivity and boundedness of the solution of the system are discussed. The existence and stability of the biologically feasible equilibrium points are investigated. Numerical simulations are performed to support our analytical findings. [ABSTRACT FROM AUTHOR]

Considering that the ecological system is often deeply perturbed by human exploiting activities, this paper deals with a prey-predator model with prey refuge in which both species are independently harvested. First, some sufficient conditions for global stability of equilibria are obtained, and the existence and uniqueness of limit cycles 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 equilibrium is discussed. Finally, the influences of prey refuge and harvesting efforts on equilibrium density values are considered and some numerical simulations are given to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper analyses a bionomic model of two competitive species in the presence of toxicity with different harvesting efforts. An interesting dynamics in the first quadrant is analysed and two saddle-node bifurcations are detected for different bifurcation parameters. It is noted that under certain parametric restrictions, the model has a unique positive equilibrium point that is globally asymptotically stable whenever it is locally stable. It is also noted that the model can have zero, one or two feasible equilibria appearing through saddle-node bifurcations. The non-existence of a limit cycle in the interior of the first quadrant is also discussed using the Poincare–Dulac criteria. The saddle-node bifurcations are studied using Sotomayor's theorem. Numerical simulations are carried out to validate the analytical findings. The conditions for the existence of bionomic equilibria are discussed and an optimal harvesting policy is derived using Pontryagin's maximum principle. [ABSTRACT FROM PUBLISHER]

Highlights • We explores the influence of harvesting (or culling) on the outcome of the competition of two species in a spatially heterogeneous environment, presenting sufficient conditions for coexistence or competitive exclusion. • If the only difference between the two competing populations is a diffusion strategy, we explore how harvesting can either promote coexistence or lead one of the species to extinction. • If, without harvesting, the two species coexist, we evaluate the relation of harvesting rates that keep the coexistence pattern, as well as give sufficient estimates when one of the competitors goes extinct. All the results are illustrated with numerical simulations, including sharpness of estimates. Abstract The paper explores the influence of harvesting (or culling) on the outcome of the competition of two species in a spatially heterogeneous environment. The harvesting effort is assumed to be proportional to the space-dependent intrinsic growth rate. The differences between the two populations are the diffusion strategy and the harvesting intensity. In the absence of harvesting, competing populations may either coexist, or one of them may bring the other to extinction. If the latter is the case, introduction of any level of harvesting to the successful species guarantees survival to its non-harvested competitor. In the former case, there is a strip of "close enough" to each other harvesting rates leading to preservation of the original coexistence. Some estimates are obtained for the relation of the harvesting levels providing either coexistence or competitive exclusion. [ABSTRACT FROM AUTHOR]

In this paper a predator-prey model with discrete delay and harvesting of predator is proposed and analyzed by considering ratio-dependent functional response. Conditions of existence of various equilibria and their stability have been discussed. By taking delay as a bifurcation parameter, the system is found to undergo a Hopf bifurcation. Numerical simulations are also performed to illustrate the results. [ABSTRACT FROM AUTHOR]

This paper aims to study the effect of time-delay and combined harvesting on a Michaelis-Menten type ratio-dependent predator-prey system. Dynamical behaviors such as persistence, stability, bifurcation, et cetera, are studied critically. Computer simulations are carried out to illustrate our analytical findings. [ABSTRACT FROM AUTHOR]