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Dynamics and chaos control for a novel model incorporating plant quality index and larch budmoth interaction

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  • Din, Qamar

Abstract

In this paper, we study some dynamics concerning the interaction of budmoth and plant quality index of larch situated in the Swiss Alps. Taking into account this interaction, a two-dimensional discrete-time system is formulated and discussed. The new model is formulated with an application of Holling type III functional response for the plant quality index. Furthermore, the proposed functional response is supported by actual observed data related to larch budmoth interaction. In addition to proving that solutions are uniformly bounded, the existence of biologically feasible fixed points and the local dynamics of the proposed model regarding its fixed points are also studied. It is shown that the proposed model undergoes period-doubling bifurcation around its coexistence with the implementation of the center manifold and normal form theories. Furthermore, the existence and direction of Neimark–Sacker bifurcation about positive fixed point are discussed. Taking into account the biological relevance of chaos control strategies, different methods of controlling chaos are implemented with their biological relevance. Numerical simulation is demonstrated to illustrate the theoretical discussion. Finally, theoretical discussion is validated with experimental and field data.

Suggested Citation

  • Din, Qamar, 2021. "Dynamics and chaos control for a novel model incorporating plant quality index and larch budmoth interaction," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921009498
    DOI: 10.1016/j.chaos.2021.111595
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    1. Qamar Din & A. A. Elsadany & Hammad Khalil, 2017. "Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-15, April.
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