Applied Analysis in Biological and Physical Sciences: by Jim M. Cushing, M. Saleem, H. M. Srivastava, Mumtaz Ahmad

By Jim M. Cushing, M. Saleem, H. M. Srivastava, Mumtaz Ahmad Khan, M. Merajuddin

The publication includes contemporary advancements and modern study in mathematical research and in its program to difficulties bobbing up from the organic and actual sciences. The e-book is of curiosity to readers who desire to study of latest study in such themes as linear and nonlinear research, mathematical biology and ecology, dynamical structures, graph concept, variational research and inequalities, practical research, differential and distinction equations, partial differential equations, approximation conception, and chaos.
All papers have been ready by way of contributors on the overseas convention on fresh Advances in Mathematical Biology, research and functions (ICMBAA-2015) held in the course of 4–6 June 2015 in Aligarh, India. A focal subject matter of the convention was once the appliance of arithmetic to the organic sciences and on present examine in components of theoretical mathematical research that may be used as refined instruments for the learn of clinical difficulties. The convention supplied researchers, academicians and engineers with a platform that inspired them to switch their cutting edge principles in mathematical research and its purposes in addition to to shape interdisciplinary collaborations.
The content material of the e-book is split into 3 elements: half I includes contributions from members whose issues are on the topic of nonlinear dynamics and its purposes in organic sciences. half II has contributions which predicament themes on nonlinear research and its purposes to numerous difficulties in technology, engineering and undefined. half III includes contributions facing a few difficulties in utilized analysis.

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These are called blue-sky bifurcations (or saddlenode or tangent bifurcations). Thus, in the neighborhood of blue-sky bifurcations the lower (decreasing) segment of C will contain unstable equilibria while the upper (increasing) segment of C will have stable equilibria. See Fig. 1. We note that a backward bifurcation creates the possibility that positive stable equilibria (or other kinds of attractors) can occur for r0 < 1 when the extinction equilibrium is also stable. Such multiple attractor scenarios, where one attractor is extinction and the other is non-extinction, is called a strong Allee effect [4].

Ser. A : Math. Anal. 15, 897–906 (2008) 9. : Turing and Hopf patterns formation in a predator-prey model with Leslie-Gower-type functional response. Dyn. Contin. Discret. Impuls. Syst. Ser. B 16(4), 479–488 (2009) 10. : On a nonlinear non-autonomous predator-prey model with diffusion and distributed delay. J. Comput. Appl. Math. 180, 33–49 (2005) 11. : On the dynamics of a predator-prey model with the Holling-Tanner functional, Editor V. Capasso. In: Proceedings of the ESMTB Conference, pp. 270–278 (2002) 12.

Parameters α, β, γ and δ can be interpreted as dimensionless and rescaled grazing rate of prey by their specialist predators, growth rate of predators, death rate of predators and intra-specific competition rate among the predators respectively (see [5] for details). This model can be considered as an extension of the classical Bazykin type prey-predator model [9] with ratio-dependent functional response. Above model exhibits a wide variety of dynamic behavior and undergoes several types of local and global bifurcations which are related to the stable/oscillatory coexistence of the prey and the predator as well as to the extinction of both populations [5].

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