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<p>This study investigates how ecotourism and time delays affect the conservation of forestry biomass using a nonlinear mathematical model. It examines the relationships among forestry biomass, industrialisation pressure, and technological progress. By pinpointing critical delay parameter values in specific dynamic scenarios, the research evaluates the system’s stability when these values are below or above certain thresholds. The analysis highlights the possibility of a Hopf bifurcation as delay parameters cross critical values, leading to notable changes in system behaviour. Additionally, different parametric controls reveal interesting dynamical features. Using normal form theory and the centre manifold theorem, the study forecasts the stability and evolution of bifurcating periodic solutions. Numerical simulations support these theoretical conclusions, providing actual demonstration for the parameters.</p>

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Stability and Direction of the Bifurcating Parameter in a Nonlinear Conservation Model Admitting Ecotourism

  • 期刊论文

  • 发表日期：

    2026年7月27日

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  • Harendra Verma,
  • Rachana Pathak,
  • Archana Singh Bhadauria,
  • Pankaj Mathur,
  • Manisha Chaudhary,
  • Naveen Sharma,
  • Manju Agrawal

摘要

This study investigates how ecotourism and time delays affect the conservation of forestry biomass using a nonlinear mathematical model. It examines the relationships among forestry biomass, industrialisation pressure, and technological progress. By pinpointing critical delay parameter values in specific dynamic scenarios, the research evaluates the system’s stability when these values are below or above certain thresholds. The analysis highlights the possibility of a Hopf bifurcation as delay parameters cross critical values, leading to notable changes in system behaviour. Additionally, different parametric controls reveal interesting dynamical features. Using normal form theory and the centre manifold theorem, the study forecasts the stability and evolution of bifurcating periodic solutions. Numerical simulations support these theoretical conclusions, providing actual demonstration for the parameters.