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Dynamic Complexities in a Pest Control Model with Birth Pulses

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Applied Analysis in Biological and Physical Sciences

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 186))

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Abstract

In this paper, an impulsive system of differential equations is proposed to model a pest control system. The stage-structured system consists of immature and mature pest population. Birth pulses occur at regular intervals to release immature pest. The pest is controlled by spraying chemical pesticides affecting both immature and mature pest. The stroboscopic map of the impulsive system is analyzed for the stability of pest-free and non-trivial period-1 solution. Numerical simulations with MATLAB reveal the complex dynamical behavior. Period doubling cascade, chaos and period halving bifurcations are observed above the threshold level.

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Acknowledgements

The first author expresses thanks to Ministry of Human Resources and Development (MHRD), India for providing financial support without which this research effort would not be possible.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee (IITR), Roorkee, Uttarakhand, 247667, India

    Anju Goel & Sunita Gakkhar

Authors
  1. Anju Goel
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  2. Sunita Gakkhar
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Corresponding author

Correspondence to Anju Goel .

Editor information

Editors and Affiliations

  1. University of Arizona Dept. of Mathematics, Tucson, USA

    Jim M. Cushing

  2. Department of Applied Mathematics, Aligarh Muslim University Department of Applied Mathematics, Aligarh, Uttar Pradesh, India

    M. Saleem

  3. Department of Mathematics and Statistics, University of Victoria, VICTORIA, British Columbia, Canada

    H. M. Srivastava

  4. Department of Applied Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, India

    Mumtaz Ahmad Khan

  5. Department of Applied Mathematics, Aligarh Muslim University, Aligarh, India

    M. Merajuddin

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Goel, A., Gakkhar, S. (2016). Dynamic Complexities in a Pest Control Model with Birth Pulses. In: Cushing, J., Saleem, M., Srivastava, H., Khan, M., Merajuddin, M. (eds) Applied Analysis in Biological and Physical Sciences. Springer Proceedings in Mathematics & Statistics, vol 186. Springer, New Delhi. https://doi.org/10.1007/978-81-322-3640-5_5

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