Journal ArticleDOI
Bifurcation and optimal harvesting of a diffusive predator–prey system with delays and interval biological parameters ☆
Xuebing Zhang,Hongyong Zhao +1 more
TLDR
Numerical evidence shows that the presence of harvesting can impact the existence of species and over harvesting can result in the extinction of the prey or the predator which is in line with reality.About:
This article is published in Journal of Theoretical Biology.The article was published on 2014-12-21. It has received 44 citations till now. The article focuses on the topics: Saddle-node bifurcation & Transcritical bifurcation.read more
Citations
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Journal ArticleDOI
Stability and bifurcation analysis in a predator–prey system with Michaelis–Menten type predator harvesting
Dongpo Hu,Hongjun Cao +1 more
TL;DR: In this article, the stability and bifurcation analysis for a predator-prey system with the nonlinear Michaelis-Menten type predator harvesting are taken into account, and the existence and stability of possible equilibria are investigated.
Journal ArticleDOI
Patterns induced by super cross-diffusion in a predator-prey system with Michaelis-Menten type harvesting
Biao Liu,Ranchao Wu,Liping Chen +2 more
TL;DR: Turing instability and pattern formation in a super cross-diffusion predator-prey system with Michaelis-Menten type predator harvesting are investigated and amplitude equations near the Turing bifurcation point for the excited modes are derived by means of weakly nonlinear theory.
Journal ArticleDOI
The diffusive Lotka-Volterra predator-prey system with delay.
TL;DR: The Galerkin method is applied, which approximates the spatial structure of both the predator and prey populations, and this approach is used to obtain a lower-order, ordinary differential delay equation model for the system of governing delay partial differential equations.
Journal ArticleDOI
Stability and bifurcation analysis in a delayed reaction-diffusion malware propagation model
TL;DR: Numerical evidence shows that the spatial-temporal dynamic characteristics of malware propagation in MWSNs are closely related to the packet transmission rate, the communication rang and the mobile behavior of nodes.
Journal ArticleDOI
Dynamical analysis of a fuzzy phytoplankton–zooplankton model with refuge, fishery protection and harvesting
Xin-You Meng,Yu-Qian Wu +1 more
TL;DR: In this paper, a singular phytoplankton-zooplankton model with fuzzy parameters, refuge, fishery protection and harvesting is studied by regarding the imprecise biological parameters as one form of triangular fuzzy number.
References
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Book
Theory and Applications of Partial Functional Differential Equations
TL;DR: In this paper, the existence and compactness of solution semiflows of linear systems are investigated. But the authors focus on the nonhomogeneous systems and do not consider the linearized stability of non-homogeneous solutions.
Journal ArticleDOI
Fluctuations in the Abundance of a Species considered Mathematically
TL;DR: In this paper, Lotka observed that he had obtained the differential equations in the case of two species, one of which feeds upon the other, and that he gave, as well as myself, the same diagram of the integral, and also the period in the cases of small fluctuations.
Book
Discourse on method and The meditations
René Descartes,F. E. Sutcliffe +1 more
TL;DR: Rene Descartes as discussed by the authors was a central figure in the scientific revolution of the seventeenth century and outlined the contrast between mathematics and experimental sciences, and the extent to which each one can achieve certainty.
Journal ArticleDOI
Instabilities in spatially extended predator–prey systems: Spatio-temporal patterns in the neighborhood of Turing–Hopf bifurcations
TL;DR: A generalized predator-prey system on a spatial domain is studied, where diffusion is considered as the principal process of motion and the conditions for Hopf and Turing instabilities without specifying the predator- prey functional responses are derived.
Journal ArticleDOI
Optimal harvesting and stability for a two-species competitive system with stage structure.
Xinyu Song,Lansun Chen +1 more
TL;DR: A stage-structured competitive population model with two life stages, immature and mature, with a mature population of harvesting with conditions for the existence of a globally asymptotically stable positive equilibrium and a threshold of harvesting for the mature population is considered.
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