The Study of a Predator-Prey Model with Fear Effect Based on State-Dependent Harvesting Strategy

In presence of predator population, the prey population may significantly change their behavior. Fear for predator population enhances the survival probability of prey population, and it can greatly reduce the reproduction of prey population. In this study, we propose a predator-prey fishery model introducing the cost of fear into prey reproduction with Holling type-II functional response and prey-dependent harvesting and investigate the global dynamics of the proposed model. For the system without harvest, it is shown that the level of fear may alter the stability of the positive equilibrium, and an expression of fear critical level is characterized. For the harvest system, the existence of the semitrivial order-1 periodic solution and positive order- q ( q ≥ 1 ) periodic solution is discussed by the construction of a Poincaré map on the phase set, and the threshold conditions are given, which can not only transform state-dependent harvesting into a cycle one but also provide a possibility to determine the harvest frequency. In addition, to ensure a certain robustness of the adopted harvest policy, the threshold condition for the stability of the order- q periodic solution is given. Meanwhile, to achieve a good economic profit, an optimization problem is formulated and the optimum harvest level is obtained. Mathematical findings have been validated in numerical simulation by MATLAB. Different effects of different harvest levels and different fear levels have been demonstrated by depicting figures in numerical simulation using MATLAB.

Complex Dynamical Behavior of Holling–Tanner Predator-Prey Model with Cross-Diffusion

Spatial predator-prey models have been studied by researchers for many years, because the exact distributions of the population can be well illustrated via pattern formation. In this paper, amplitude equations of a spatial Holling–Tanner predator-prey model are studied via multiple scale analysis. First, by amplitude equations, we obtain the corresponding intervals in which different kinds of patterns will be onset. Additionally, we get the conclusion that pattern transitions of the predator are induced by the increasing rate of conversion into predator biomass. Specifically, pattern transitions of the predator between distinct Turing pattern structures vary in an orderly manner: from spotted patterns to stripe patterns, and finally to black-eye patterns. Moreover, it is discovered that pattern transitions of prey can be induced by cross-diffusion; that is, patterns of prey transmit from spotted patterns to stripe patterns and finally to a mixture of spot and stripe patterns. Meanwhile, it is found that both effects of cross-diffusion and interaction between the prey and predator can lead to the complicated phenomenon of dynamics in the system of biology.

Sistem Predasi dalam Dinamika Populasi

Paper ini berkaitan dengan system predasi dalam Dinamika Populasi. Paper ini disusun dalam memperluas ilmu tentang dasar dan manfaat pembelajaran dinamika populasiberdasarkan pengamatan dari berbagai sumber informasi yang dijadikan sebagai referensi. Semoga paper ini dapat memberikan wawasan yang lebih luas dan menjadi sumbangan pemikiran kepada pembaca khususnya para mahasiswa. Predasi merupakan hubunganantara predator (pemangsa) dan prey (mangsa). Pada predasi sendiri terdapat dua model yang mendeskripsikan interaksi dua spesies terdiri dari predator dan prey merupakanmodel predator-prey. Model predator- prey sederhana ini diperkenalkan Lotka- Voltera yang kemudian di modifikasi oleh Leslie Gower. Hubungan antar spesies dapat dikelompokkan menjadi netralisme, mutualisme, parasitisme, predatorisme, kooperasi, kompetisi, komensalisme, dan antagonis.

A delay nonautonomous model for the effects of fear and refuge on predator–prey interactions with water-level fluctuations

The interaction of prey (small fish) and predator (large fish) in lakes/ponds at temperate and tropical regions varies when water level fluctuates naturally during seasonal time. We relate the perceptible effect of fear and anti-predator behavior of prey with the water-level fluctuations and describe how these are influenced by the seasonal changing of water level. So, we consider these as time-dependent functions to make the system more realistic. Also, we incorporate the time-dependent delay in the negative growth rate of prey in predator–prey model with Crowley–Martin-type functional response. We clearly provide the basic dynamics of the system such as positiveness, permanence and nonpersistence. The existence of positive periodic solution is studied using Continuation theorem, and suffiecient conditions for globally attractivity of positive periodic solution are also derived. To make the system more comprehensive, we establish numerical simulations, and compare the dynamics of autonomous and nonautonomous systems in the absence as well as the presence of time delay. Our results show that seasonality and time delay create the occurrence of complex behavior such as prevalence of chaotic disorder which can be potentially suppressed by the cost of fear and prey refuge. Also, if time delay increases, then system leads a boundary periodic solution. Our findings assert that the predation, fear of predator and prey refuge are correlated with water-level variations, and give some reasonable biological interpretations for persistence as well as extinction of species due to water-level variations.

Discretization, Bifurcation and Control for a Class of Predator–Prey Interactions

The present study focuses on the dynamical aspects of a discrete-time Leslie–Gower predator–prey model accompanied by a Holling type III functional response. Discretization is conducted by applying a piecewise constant argument method of differential equations. Moreover, boundedness, existence, uniqueness, and a local stability analysis of biologically feasible equilibria were investigated. By implementing the center manifold theorem and bifurcation theory, our study reveals that the given system undergoes period-doubling and Neimark–Sacker bifurcation around the interior equilibrium point. By contrast, chaotic attractors ensure chaos. To avoid these unpredictable situations, we establish a feedback-control strategy to control the chaos created under the influence of bifurcation. The fractal dimensions of the proposed model are calculated. The maximum Lyapunov exponents and phase portraits are depicted to further confirm the complexity and chaotic behavior. Finally, numerical simulations are presented to confirm the theoretical and analytical findings.

Dynamics and bifurcations of a ratio-dependent predator-prey model

In this paper, we study a ratio-dependent predator-prey model with modied Holling-Tanner formalism, by using dynamical techniques and numerical continuation algorithms implemented in Matcont. We determine codim-1 and 2 bifurcation points and their corresponding normal form coecients. We also compute a curve of limit cycles of the system emanating from a Hopf point.

Hopf bifurcation analysis in a stage-structure predator–prey model with two time delay

In this paper, we consider a predator-prey system with two time delays, which describes a prey–predator model with parental care for predators. The local stability of the positive equilibrium is analysed. By choosing the two time delays as the bifurcation parameter, the existence of Hopf bifurcation is studied. Numerical simulations show the positive equilibrium loses its stability via the Hopf bifurcation when the time delay increases beyond a threshold.

Analytical Models to Characterize Trade-Offs between Technological Upgrading and Innovation

We propose two analytical models to characterize the relationship between technological upgrading and innovation in the oil & gas industry. The first one is an “optimization model” which focuses on the trade-offs between profit maximization and environmental compliance cost. The other has been developed based on “predator-prey” model which captures the dynamics of biological systems. Our study contributes to the strategic planning process for sustainable development by providing the insight that optimal allocation process is determined by multiple operational factors, including a firm’s competitive ranking among its industrial competitors, industrial consent on the concurrent rate of return on capital investment, the projected demand of oil & gas in future, and a change in environmental compliance cost. Further, we add to the robustness of the optimal allocation process by providing binding conditions of the set of solutions.