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The Behavior of Logistic Equation with Alley Effect in Fuzzy Environment: Fuzzy Differential Equation Approach

  • Soheil Salahshour
  • Ali Ahmadian
  • Animesh Mahata
  • Sankar Prasad Mondal
  • Shariful Alam
Original Paper
First Online:

Abstract

In this paper a fuzzy logistic equation with alley effect is introduced by considering some parameter as fuzzy numbers. Due to presence of the fuzzy number the corresponding differential equation in logistic equation model with alley effect becomes fuzzy differential equation. Considering generalized Hukuhara derivative approach the fuzzy logistic equation converted to system of two crisp differential equations. We obtain the conditions of stability criterion for different cases. Different numerical examples are given to support our work.

Keywords

Logistic equation Allee effect Fuzzy differential equation Fuzzy stability analysis 
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Copyright information

© Springer (India) Private Ltd., part of Springer Nature 2018

Authors and Affiliations

  • Soheil Salahshour
    • 1
  • Ali Ahmadian
    • 2
  • Animesh Mahata
    • 3
    • 4
  • Sankar Prasad Mondal
    • 5
  • Shariful Alam
    • 4
  1. 1.Young Researchers and Elite Club, Mobarakeh BranchIslamic Azad UniversityMobarakehIran
  2. 2.Institute for Mathematical ResearchUniversity Putra Malaysia (UPM)SerdangMalaysia
  3. 3.Department of MathematicsNetaji Subhash Engineering CollegeKolkataIndia
  4. 4.Department of MathematicsIndian Institute of Engineering Science and Technology, ShibpurHowrahIndia
  5. 5.Department of MathematicsMidnapore College (Autonomous), MidnaporeWest MidnaporeIndia

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