SPATIOTEMPORAL DYNAMICS IN A PREDATOR-PREY MODEL WITH A FUNCTIONAL RESPONSE INCREASING IN BOTH PREDATOR AND PREY DENSITIES

Ruizhi Yang; Yuting Ding

doi:10.11948/20190295

2020 Volume 10 Issue 5

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Ruizhi Yang, Yuting Ding. SPATIOTEMPORAL DYNAMICS IN A PREDATOR-PREY MODEL WITH A FUNCTIONAL RESPONSE INCREASING IN BOTH PREDATOR AND PREY DENSITIES[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 1962-1979. doi: 10.11948/20190295

Citation:

Ruizhi Yang, Yuting Ding. SPATIOTEMPORAL DYNAMICS IN A PREDATOR-PREY MODEL WITH A FUNCTIONAL RESPONSE INCREASING IN BOTH PREDATOR AND PREY DENSITIES[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 1962-1979. doi: 10.11948/20190295

SPATIOTEMPORAL DYNAMICS IN A PREDATOR-PREY MODEL WITH A FUNCTIONAL RESPONSE INCREASING IN BOTH PREDATOR AND PREY DENSITIES

Ruizhi Yang¹,
Yuting Ding^1, ,

1.
Department of Mathematics, Northeast Forestry University, 26 Hexing Road, 150040 Harbin, China

Corresponding author: Email address: yuting840810@163.com(Y. Ding)
Fund Project: The authors were supported by Fundamental Research Funds for the Central Universities (2572019BC01), Natural Science Foundation of Heilongjiang (A2018001), Postdoctoral Science Foundation of China (2019M651237) and National Nature Science Foundation of China (11601070)

Abstract

Abstract

In this paper, we studied a diffusive predator-prey model with a functional response increasing in both predator and prey densities. The Turing instability and local stability are studied by analyzing the eigenvalue spectrum. Delay induced Hopf bifurcation is investigated by using time delay as bifurcation parameter. Some conditions for determining the property of Hopf bifurcation are obtained by utilizing the normal form method and center manifold reduction for partial functional differential equation.
- Predator-prey /
- delay /
- Turing instability /
- Hopf bifurcation
MSC: 34K18, 35B32

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References

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