Stability and Hopf bifurcation for a competition and cooperation model of two enterprises with delay

Abstract In this manuscript, we first consider the diffusive competition and cooperation system subject to Neumann boundary conditions without delay terms and get the conclusion that the unique positive constant equilibrium is locally asymptotically stable. Then, we study the diffusive delayed competition and cooperation system subject to Neumann boundary conditions, and the existence of Hopf bifurcation at the positive equilibrium is obtained by regarding delay term as the parameter. By the theory of center manifold and normal form, an algorithm for determining the direction and stability of Hopf bifurcation is derived. Finally, some numerical simulations and summarizations are carried out for illustrating the theoretical analytic results.

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The Study of the Competition Model of Portal and Search Engine

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.50-51.442 ◽

2011 ◽

Vol 50-51 ◽

pp. 442-446

Author(s):

Jing Guo Qu ◽

Dong Hua Wang ◽

Yu Huan Cui ◽

Ya Mian Peng

Keyword(s):

Search Engine ◽

Competition Model ◽

Predator Prey ◽

Competition And Cooperation ◽

Predator Prey Model ◽

Prey Model ◽

Stability Model ◽

Cooperation Model ◽

Mutualism Model ◽

Building Stability

This paper is to discuss the competition and cooperation of portal and search engine mainly by building stability model. We can use Lotka-Volterra mutualism model to describe and build cooperation model of portal and search engine, and we can use Lotka-Volterra predator – prey model with Logistic items to describe and build competition model of portal and search engine.

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Competition and Cooperation Relationships of Multi-category Ports Based on the Improved L-V Model

E3S Web of Conferences ◽

10.1051/e3sconf/20197903008 ◽

2019 ◽

Vol 79 ◽

pp. 03008

Author(s):

Zhiyi Lei ◽

Yifan Zhu ◽

Liling Chen

Keyword(s):

Mutual Influence ◽

Coefficient Matrix ◽

Volterra Model ◽

Average Growth ◽

Competition And Cooperation ◽

Growth Space ◽

Cooperation Model ◽

Cargo Throughput ◽

Cooperation Relationship ◽

Relationship Of

The improved Lotka-Volterra model for the multi-goods of the multi-ports is proposed based on the competition of kinds of ecological populations in nature. Based on the analysis of the current throughput, annual average growth rate, potential throughput growth space, and the impacts of other port cargo throughput, the model establishes a competition coefficient matrix to determine the competitive cooperation model between different ports. The model is used to analyze the competition and cooperation relationship of different cargo types in four ports of Fujian. The results show that the model can reflect the mutual influence mechanism of competition and collaboration of multiple types of cargo in multiple ports, which can provide an effective and targeted basis for optimizing the cargo structure of ports and improving the competitive relationship of the ports.

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