Computational dynamics of the Nicholson-Bailey models

Sk. Sarif Hassan; Divya Ahluwalia; Ravi Kiran Maddali; Monika Manglik

doi:10.1140/epjp/i2018-12164-1

EPJ

Computational dynamics of the Nicholson-Bailey models

Sk. Sarif Hassan¹, Divya Ahluwalia², Ravi Kiran Maddali²^* and Monika Manglik²

¹ Department of Mathematics, Pingla Thana Mahavidyalaya, Medinipur, West Bengal, India
² Department of Mathematics, School of Engineering, University of Petroleum and Energy Studies, Bidholi, Dehradun, India

Received: 24 June 2018
Accepted: 23 July 2018
Published online: 4 September 2018

Abstract

In population dynamics, the Nicholson-Bailey model describes the host-parasitoid system which has been well studied since 1930 with a consideration that the parameters are all positive real numbers. In this article, the dynamics of the Nicholson-Bailey model $x_{n+1} = x_{n} (e^{r(1-\frac{x_{n}}{\kappa}) - ay_{n}})$ and $y_{n+1} = x_{n} (1-e^{-ay_{n}})$ is reinvestigated computationally where all the parameters are considered as real numbers. The model has all sorts of dynamical behavior such as chaotic, periodic and locally stable/unstable equilibriums. In addition, the dynamics of the scaled Nicholson-Bailey $x_{n+1}=(x_{n} + \alpha) (e^{r(1-\frac{(x_{n}+\alpha)}{\kappa})-a(y_{n}+\beta)})$ , $y_{n+1}=(x_{n} +\alpha) (1-e^{-a(y_{n}+\beta)})$ where $\alpha$ and $\beta$ are scaling factors and of the noisy model $x_{n+1}=x_{n} (e^{r(1-\frac{x_{n}}{\kappa})-ay_{n}})+\nu_{1}$ , $y_{n+1}=x_{n} (1-e^{-ay_{n}})+\nu_{2}$ , where $(\nu_{1}, \nu_{2})$ is uniformly distributed noise over the interval (0,1), are also reconnoitered computationally.

12 Internat. Congress of the Balkan Physical Union
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EPJ

Computational dynamics of the Nicholson-Bailey models

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