2014
DOI: 10.1007/s12190-014-0822-1
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Abstract: In this paper, we investigate the effect of mutual interference on the dynamics of a predator-prey system with gestation delay. It has been observed that there is stability switches and system becomes unstable due to the combine effect of mutual interference and time delay. We determine the conditions under which the model system becomes globally asymptotically stable around the non-zero equilibria. By applying the normal form theory and the center manifold theorem, the explicit formulae which determine the st… Show more

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Cited by 9 publications
(5 citation statements)
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References 22 publications
(23 reference statements)
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“…Assume that 0 < m 2 ≤ 1, as per literature on mutual interference [1,2]. In this paper, we consider the general logistic growth and the generalized Holling type functional response, see [3,4]:…”
Section: Model Formulationmentioning
confidence: 99%
See 1 more Smart Citation
“…Assume that 0 < m 2 ≤ 1, as per literature on mutual interference [1,2]. In this paper, we consider the general logistic growth and the generalized Holling type functional response, see [3,4]:…”
Section: Model Formulationmentioning
confidence: 99%
“…of model(3), we obtain the following two interior equilibrium points E1 2 (3.12437, 30.6886) and E 2 2 (6.67563, 31.7032) and the predator-free equilibrium point is E 1 (10, 0). The eigenvalues associated with E 1 2 (3.12437, 30.6886) are −0.343043 and 0.170265, hence E 1 2 is a saddle.…”
mentioning
confidence: 92%
“…the effect of delay on both two and three species predator-prey models. Upadhyay and Agrawal [55] investigated the effect of mutual interference on the dynamics of delay induced predator prey system, and determined the conditions under which the model becomes globally asymptotically stable around the nonzero equilibria. Recently, Jana et al [56] have made an attempt to understand the role of top predator interference and gestation delay on the dynamics of a three species food chain model.…”
Section: Effect Of Time Delaymentioning
confidence: 99%
“…This delay can be the delay of gestation period, 17 delay of maturation, 18 delay of immune system to respond, 19 and so forth. In biological and ecological modeling, many authors have studied the effect of a time delay in many mathematical models and shown the existence of Hopf bifurcation which is an important characteristic of a delay differential equation 20‐22 …”
Section: Introductionmentioning
confidence: 99%
“…In biological and ecological modeling, many authors have studied the effect of a time delay in many mathematical models and shown the existence of Hopf bifurcation which is an important characteristic of a delay differential equation. [20][21][22] The theory of fractional calculus, a generalization of integral order differentiation and integration, has been developed fruitfully in the past few years. Fractional-order differential equations (FODEs) are related to systems with memory which exists in most biological systems and consequently it is claimed that FODEs are, at least, as stable as their integer-order counterpart.…”
mentioning
confidence: 99%