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Analysis of the Stochastic Population Model with Random Parameters.

Adeeb Noor1, Ahmed Barnawi1, Redhwan Nour2

  • 1Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah 21589, Saudi Arabia.

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|December 8, 2020
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Summary

This study introduces a spectral technique to analyze complex population models with random environmental factors. The method effectively handles uncertainties, providing insights into population dynamics for conservation and invasion studies.

Keywords:
population modelsrandom parameterssensitivity analysisstochastic processesvariance decomposition

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Environmental Science

Background:

  • Population models are crucial for understanding environmental dynamics, biological invasions, and conservation efforts.
  • Incorporating stochasticity and random variations significantly complicates these models.
  • Existing techniques struggle to effectively manage mixed sources of uncertainty in population dynamics.

Purpose of the Study:

  • To develop and present a novel spectral technique for analyzing stochastic population models with random parameters.
  • To address models with mixed sources of uncertainty, including noise and uncertain parameters.
  • To provide a method for separating and evaluating the contributions of different uncertainty sources.

Main Methods:

  • A spectral technique utilizing spectral decompositions for various randomness types is proposed.
  • A deterministic system is derived by leveraging the statistical properties of random bases.
  • This derived deterministic system can be analyzed using classical analytical or numerical methods.

Main Results:

  • The spectral technique demonstrates high convergence rates.
  • The method successfully separates contributions from different sources of uncertainty.
  • Sensitivity indices for uncertain parameters can be reliably evaluated.

Conclusions:

  • The presented spectral technique offers an effective approach for analyzing complex stochastic population models.
  • This method provides a significant advantage over existing techniques by enabling clear separation of uncertainty contributions.
  • The approach is broadly applicable to diverse complex systems with stochastic and random parameters.