Stability analysis and optimal impulsive harvesting for a delayed stage-structured self dependent two compartment commercial fishery model

2021 ◽  
Author(s):  
Amit Sharma ◽  
Bhanu Gupta ◽  
Joydip Dhar ◽  
Sanjay K. Srivastava ◽  
Payal Sharma
Keyword(s):  
Stability Analysis ◽  
Commercial Fishery ◽  
Fishery Model ◽  
Impulsive Harvesting

HETEROCLINIC BIFURCATIONS OF A PREY–PREDATOR FISHERY MODEL WITH IMPULSIVE HARVESTING

2013 ◽  
Vol 06 (05) ◽  
pp. 1350031 ◽  
Author(s):  
CHUNJIN WEI ◽  
LANSUN CHEN
Keyword(s):  
Dynamic Systems ◽  
Vector Fields ◽  
Sufficient Conditions ◽  
Heteroclinic Cycle ◽  
Heteroclinic Bifurcation ◽  
Perturbed System ◽  
State Dependent ◽  
Continuous Dynamic ◽  
Fishery Model ◽  
Impulsive Harvesting

In this paper, we consider a prey–predator fishery model with Allee effect and state-dependent impulsive harvesting. First, we investigate the existence of order-1 heteroclinic cycle. Second, choosing p as a control parameter, we obtain the sufficient conditions for the existence and uniqueness of order-1 periodic solution of system (2.3) by using the geometry theory of semi-continuous dynamic systems. Finally, on the basis of the theory of rotated vector fields, heteroclinic bifurcation to perturbed system of system (2.3) is also studied. The methods used in this paper are novel to prove the existence of order-1 heteroclinic cycle and heteroclinic bifurcations.

IMPULSIVE SELECTIVE HARVESTING IN A LOGISTIC FISHERY MODEL WITH TIME DELAY

2006 ◽  
Vol 14 (01) ◽  
pp. 91-99 ◽  
Author(s):  
YONGZHEN PEI ◽  
LANSUN CHEN ◽  
CHANGGUO LI ◽  
CHUNHUA WANG
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Positive Periodic Solution ◽  
Critical Value ◽  
Asymptotically Stable ◽  
Selective Harvesting ◽  
Fishery Model ◽  
Impulsive Harvesting

In this work, we consider a logistic fishery model and discuss the selective impulsive harvesting of fish above a certain age or size by incorporating a time delay in the impulsive harvesting term. It is proved that there exists an asymptotically stable positive periodic solution [Formula: see text] when the catchability coefficient h is less than some critical value [Formula: see text]. It is concluded that [Formula: see text] and [Formula: see text] are increasing with respect to l. Simulations shows that the delayed harvesting is advantageous to the sustainability of the population.

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