Existence and Uniqueness of Strong Solution for Predator-Prey System of Three Species with Age-Structure

2011 ◽  
pp. 590-601
Author(s):  
Chen Li-Yu ◽  
Zhang Qi-Min
Keyword(s):  
Strong Solution ◽  
Age Structure ◽  
Existence And Uniqueness ◽  
Predator Prey ◽  
Prey System

Existence and Uniqueness for Stochastic Predator-Prey System of Two Species with Age-Structured

2011 ◽  
Vol 219-220 ◽  
pp. 680-684
Author(s):  
Fei Fei Li ◽  
Qi Min Zhang
Keyword(s):  
Strong Solution ◽  
Existence And Uniqueness ◽  
Population System ◽  
Predator Prey ◽  
Prey System ◽  
Age Dependent ◽  
Age Structured

In this paper we introduce a stochastic age-dependent predator-prey system. Existence and uniqueness of strong solution for a stochastic population system of two species with age-dependent are proved. The analysis uses Barkholder-Davis-Gundy’s inequality,ItÔ's formula and some special inequalities to achieve our purpose.

OPTIMAL CONTROL FOR A PREDATOR-PREY SYSTEM WITH AGE-DEPENDENT

2009 ◽  
Vol 02 (01) ◽  
pp. 45-59 ◽  
Author(s):  
ZHIXUE LU
Keyword(s):  
Optimal Control ◽  
Existence And Uniqueness ◽  
Normal Cone ◽  
Optimal Harvesting ◽  
Negative Solution ◽  
Optimal Control Strategy ◽  
Predator Prey ◽  
Prey System ◽  
Age Dependent ◽  
Existence Of Optimal Control

This paper is concerned with optimal harvesting policy for predator-prey system of three species with age-dependent. The existence and uniqueness of non-negative solution of the system are proved using the fixed pint theorem. The existence of optimal control strategy is discussed, optimality conditions are derived by means of normal cone and Dubovitskii–Milyutin's general theory. Our results extend some known criteria.

A MATHEMATICAL MODEL FOR TROPHIC INTERACTIONS IN AN ACARINE PREDATOR-PREY SYSTEM

1995 ◽  
Vol 03 (02) ◽  
pp. 303-312 ◽  
Author(s):  
G. BUFFONI ◽  
G. DI COLA ◽  
J. BAUMGÄRTNER ◽  
V. MAURER
Keyword(s):  
Mathematical Model ◽  
Existence And Uniqueness ◽  
Stability Criteria ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Special Cases ◽  
Behavioral Parameters ◽  
The Stability ◽  
Steady State Solutions

An acarine predator-prey model is introduced and some results concerning the stability of this system are derived. The existence and uniqueness of positive steady state solutions are shown, and stability criteria are estabilished in function of ecological and behavioral parameters. Some special cases include Ivlev and Lotka-Volterra predation. Theoretical and numerical results allow us to assess the feasibility of a biological control of the prey.

AN ACARINE PREDATOR–PREY POPULATION INFESTING STORED PRODUCTS

1964 ◽  
Vol 42 (4) ◽  
pp. 655-673 ◽  
Author(s):  
T. Burnett
Keyword(s):  
Age Structure ◽  
Stored Products ◽  
Tyrophagus Putrescentiae ◽  
Predator Prey ◽  
Prey System ◽  
Number Of Factors ◽  
Large Fluctuations ◽  
Blattisocius Dentriticus ◽  
Prey Populations

Populations of the stored product mite Tyrophagus putrescentiae (Schrank) and its predator Blattisocius dentriticus (Berl.) were propagated in two experimental universes. Although the predator determined the size of the prey populations, the densities of both species fluctuated with peaks of abundance occurring every 6 to 8 weeks. A number of factors modified, to some extent, the role of "predator searching" as a mechanism controlling both the average densities and fluctuations in abundance of the two species. With large fluctuations in the abundance of the prey there was a pronounced cycle in the age structure of the predator and prey populations. The larger stages of the prey were largely immune to attack by the predator. Individuals of the predator developed to about one-half their normal size when the prey were scarce. The combination of immune stages of the prey and adjustment of predators to scarcity of prey ensured the coexistence of the predator–prey system. Contamination of experimental populations by psocids was one of the major hazards in rearing the populations for extended periods.

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