Diffusion-Driven Stability Analysis of A Prey-Predator System with Holling Type-IV Functional Response

The object of the present article is to study the stability and bifurcation analysis of a prey-predator ecosystem where the predation is represented by a Holling Type-IV function. In this type of functional response, the predator's per capita rate of predation decreases due to the phenomenon of group defence among the prey. A comparative study of local stability in the presence and absence of diffusion has been performed.

[1]  Arthur E. Humphrey,et al.  Dynamics of a chemostat in which two organisms compete for a common substrate , 1977 .

[2]  John F. Andrews,et al.  A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates , 1968 .

[3]  L. Luckinbill,et al.  Coexistence in Laboratory Populations of Paramecium Aurelia and Its Predator Didinium Nasutum , 1973 .

[4]  C. Huffaker,et al.  Experimental studies on predation: Complex dispersion and levels of food in an acarine predator-prey interaction , 1963 .

[5]  M. Rosenzweig Paradox of Enrichment: Destabilization of Exploitation Ecosystems in Ecological Time , 1971, Science.

[6]  C. S. Holling,et al.  The functional response of predators to prey density and its role in mimicry and population regulation. , 1965 .

[7]  H. Laudelout,et al.  Kinetics of nitrite oxidation by Nitrobacter winogradskyi. , 1962, The Biochemical journal.

[8]  Robert M. May,et al.  Limit Cycles in Predator-Prey Communities , 1972, Science.

[9]  G S Wolkowicz,et al.  Predator-prey systems with group defence: The paradox of enrichment revisited , 1986, Bulletin of mathematical biology.

[10]  H LAUDELOUT,et al.  KINETICS OF THE NITRITE OXIDATION BY NITROBACTER WINOGRADSKYI , 1960, Journal of bacteriology.

[11]  A. Bush,et al.  The effect of time delay and growth rate inhibition in the bacterial treatment of wastewater. , 1976, Journal of theoretical biology.

[12]  John F. Riebesell PARADOX OF ENRICHMENT IN COMPETITIVE SYSTEMS , 1974 .

[13]  Homage to the red queen. II. Coevolutionary response to enrichment of exploitation ecosystems. , 1978, Theoretical population biology.

[14]  Toshimasa Yano,et al.  Dynamic behavior of the chemostat subject to substrate inhibition , 1969 .

[15]  H. I. Freedman Graphical stability, enrichment, and pest control by a natural enemy , 1976 .