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Dynamic complexities in a pest control model with birth pulses. (English) Zbl 1367.92098

Cushing, Jim M. (ed.) et al., Applied analysis in biological and physical sciences. ICMBAA, Aligarh, India, June 4–6, 2015. New Delhi: Springer (ISBN 978-81-322-3638-2/hbk; 978-81-322-3640-5/ebook). Springer Proceedings in Mathematics & Statistics 186, 83-97 (2016).
Summary: 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.
For the entire collection see [Zbl 1361.92003].

MSC:

92D25 Population dynamics (general)
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
60J85 Applications of branching processes
34D20 Stability of solutions to ordinary differential equations

Software:

Matlab
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Full Text: DOI

References:

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