BIFURCATIONS IN A DELAYED DIFFERENTIAL-ALGEBRAIC PLANKTON ECONOMIC SYSTEM

Yong Wang; Weihua Jiang

doi:10.11948/2017087

2017 Volume 7 Issue 4

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Yong Wang, Weihua Jiang. BIFURCATIONS IN A DELAYED DIFFERENTIAL-ALGEBRAIC PLANKTON ECONOMIC SYSTEM[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1431-1447. doi: 10.11948/2017087

Citation:

Yong Wang, Weihua Jiang. BIFURCATIONS IN A DELAYED DIFFERENTIAL-ALGEBRAIC PLANKTON ECONOMIC SYSTEM[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1431-1447. doi: 10.11948/2017087

BIFURCATIONS IN A DELAYED DIFFERENTIAL-ALGEBRAIC PLANKTON ECONOMIC SYSTEM

Yong Wang¹,
Weihua Jiang²

1 Department of Information Science and Technology, Tianjin University of Finance and Economics, Tianjin, 300222, China;
2 Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China

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Abstract

Abstract

This paper considers a phytoplankton-zooplankton bio-economic system with delay and harvesting, which is described by differential-algebraic equations. Local stability analysis of the system without delay reveals that a singularity-induced bifurcation phenomenon appears when a variation of the economic interest is taken into account, furthermore, a state feedback controller is designed to stabilize the system at the interior equilibrium. Then, we show that delay, which is considered in the toxic liberation, can induce stability switches, such that the positive equilibrium switches from stability to instability, to stability again and so on. Finally, some numerical simulations are performed to justify analytical findings.
- Differential-algebraic equations /
- harvesting /
- delay /
- stability switches /
- singularity-induced bifurcation
MSC: 34C23;34C25;34G15;34D20

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