Global dynamics and controllability of a harvested prey–predator system with Holling type III functional response

Abstract In recent years overexploitation and collapse of several biological resources have been seen in fisheries, forestry and wildlife. This is due to unconventional and indiscrete harvesting of the resources. Consequently there is much current concern to find principles for the control and management of resources, particularly in those circumstances where both prey and predator species are being exploited. This work illustrates the use of harvesting efforts as a control to obtain strategies for the control of a prey–predator system with Holling type III functional response.

[1]  W. Bowen,et al.  Grey seal predation on the eastern Scotian Shelf: modelling the impact on Atlantic cod , 1996 .

[2]  K. S. Chaudhuri,et al.  Dynamic optimization of combined harvesting of a two-species fishery , 1988 .

[3]  Hiroyuki Matsuda,et al.  Maximal yields from multispecies fisheries systems: rules for systems with multiple trophic levels. , 2006, Ecological applications : a publication of the Ecological Society of America.

[4]  Vito Volterra,et al.  Leçons sur la théorie mathématique de la lutte pour la vie , 1931 .

[5]  Jonathan M. Jeschke,et al.  PREDATOR FUNCTIONAL RESPONSES: DISCRIMINATING BETWEEN HANDLING AND DIGESTING PREY , 2002 .

[6]  N. Shigesada,et al.  Switching effect on the stability of the prey-predator system with three trophic levels , 1986 .

[7]  H. Matsuda,et al.  Fisheries management based on ecosystem dynamics and feedback control , 2002 .

[8]  J. Steele,et al.  The role of predation in plankton models , 1992 .

[9]  J. Beddington,et al.  Marine Mammals and Fisheries , 1986 .

[10]  Hiroyuki Matsuda,et al.  Effects of adaptive predatory and anti-predator behaviour in a two-prey—one-predator system , 1993, Evolutionary Ecology.

[11]  Gao Huiwang,et al.  Functions used in biological models and their influences on simulations , 2000 .

[12]  Hilborn,et al.  Depensation: evidence, models and implications , 2001 .

[13]  K. S. Chaudhuri,et al.  A bioeconomic model of harvesting a multispecies fishery , 1986 .

[14]  C. S. Holling.  The components of prédation as revealed by a study of small-mammal prédation of the European pine sawfly. , 1959 .

[15]  N. Shigesada,et al.  Switching effect of predation on competitive prey species. , 1979, Journal of theoretical biology.

[16]  Moxun Tang,et al.  Coexistence Region and Global Dynamics of a Harvested Predator-Prey System , 1998, SIAM J. Appl. Math..

[17]  C. Chakrabarti,et al.  A nonlinear two-species oscillatory system: bifurcation and stability analysis , 2003 .

[18]  Yang Kuang,et al.  Uniqueness of limit cycles in Gause-type models of predator-prey systems , 1988 .

[19]  R. Mohn,et al.  Why the Atlantic cod (Gadus morhua) stock off eastern Nova Scotia has not recovered , 2001 .

[20]  A. Dobson,et al.  Prevention of population cycles by parasite removal. , 1998, Science.