The European Physical Journal Plus

, 133:349

# Computational dynamics of the Nicholson-Bailey models

• Sk. Sarif Hassan
• Divya Ahluwalia
• Monika Manglik
Regular Article

## 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.

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© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

## Authors and Affiliations

• Sk. Sarif Hassan
• 1
• Divya Ahluwalia
• 2