Exploring the Dynamics of a Three-Species Eco-Epidemiological Model with Holling Type-II and Type-IV Functional Responses | Chapter 9 | Mathematics and Computer Science: Research Updates Vol. 4

In this chapter, a prey-predator eco-epidemiological model with susceptible and diseased prey is constructed and investigated. The existence, uniqueness and boundedness of the solution of the system are studied. The conditions for the local and global stability of coexistence steady state are examined. The conditions for the occurrence of Hopf bifurcation with fixed biological parameter values are investigated and also it is noticed that the bifurcation occurs by sensitive changes in the parameter values of m₃ , m₀ and α which represents the growth rate of a predator, transmission rate from infected prey to susceptible prey and half-saturation constant of predator respectively.  At last, the mathematical results are interpreted with the help of numerical simulations.

 

Author (s) Details

 

S Hariprasad
Department of Mathematics, Anurag University, Hyderabad, Telangana, India.

 

M A S Srinivas
Department of Mathematics, Jawaharlal Nehru Technological University, Telangana, India.

 

N. PhaniKumar
Department of Mathematics, Vignan Institute of Technology and Science, Telangana, India.

 

Lavanya S
Department of Humanities and Basic Sciences, Visveswaraya College of Engineering and Technology, Hyderabad, Telangana, India.

D. Manohar
Department of Mathematics, Anurag University, Hyderabad, Telangana, India.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v4/4897

Ammensalism Model with Distributed Type Delay | Chapter 4 | Recent Studies in Mathematics and Computer Science Vol. 3

 

We describe a mathematical model for the interaction between three species ecological model consists of first
(N1), second (N2) and third species (N3). The first species is preying on second, second species is ammensal on
the third. Distributed type delay is included in the interaction of first and second species. The system is
explained by couple of integro differential equations. The co-existing state is identified and also characterizes
the local, global stability analysis at this state. We provide a numerical simulation in support of stability analysis
using MATLAB and shown that the system is asymptotically stable.

Author(s) Details
Mrs. G. A. L. Satyavathi
Jawaharlal Nehru Technological University (JNTU), Kakinada, A.P., India.

Dr. A. V. Paparao
Department of Mathematics, Jawaharlal Nehru Technological University (JNTU), UCE, Vizianagaram, A.P., India.

Dr. K. Sobhan Babu
Department of Mathematics, Jawaharlal Nehru Technological University (JNTU), UCE, Narasaraopet, A.P., India.

View Book :- http://bp.bookpi.org/index.php/bpi/catalog/book/233

Conservation of Forestry Biomass with the Use of Alternative Resource: Advanced Study | Chapter 5 | International Research in Environment, Geography and Earth Science Vol.2

 The effect of the alternative resource and time delay on conservation of forestry biomass is studied by

considering a nonlinear mathematical model. In this paper interaction between forestry biomass,
industrialization pressure, toxicant pressure and technological effort is proposed and analysed. We
find out the critical values of delay parameters under different dynamical situations and observe that
system is stable and unstable when the delay parameters are below and above the critical values
respectively and there is Hopf bifurcation when delay parameters cross the critical values. System
shows these interesting dynamical features under different critical parametric restrictions. Using the
normal form theory and the center manifold theorem, we determine the stability and direction of the
bifurcating periodic solutions. Numerical simulations illustrate the analytical results.

Author(s) Details

Dr. (Mrs.) Manju Agarwal
Department of Mathematics and Astronomy, Lucknow University, Lucknow, India.

Dr. Rachana Pathak
Department of Applied Science & Humanities (Mathematics), Faculty of Engineering & Technology, University of Lucknow,
Lucknow, U.P. 226031, India.

View Book :- http://bp.bookpi.org/index.php/bpi/catalog/book/230