Discrete Dynamical Systems: With Applications in Biology

Authors

Tahmineh Azizi
Department of Mathematics, Kansas State University, Manhattan, Kansas, USA.
Bacim Alali
Department of Mathematics, Kansas State University, Manhattan, Kansas, USA.
Gabriel Kerr
Department of Mathematics, Kansas State University, Manhattan, Kansas, USA.

Synopsis

Mathematical modeling of population dynamics has been attracted by many researchers over the last few decades. Specially, exponential difference equations have been used to model the interactions between different kind of population dynamics. Among these population models, Host-Parasitoid interactions play an important role in the ecosystem. A parasitoid is an organism that feeds another organism. The host is the organism which the parasitoid feeds. We have two different approaches to model these interactions, discrete and continuous. However, the discrete time models governed by difference equations are more realistic, rational and applicable rather than the continuous systems specially when the populations follow the non-overlapping generations. A well-known example of this non-overlapping is Insects which adults lay eggs in spring/summer and then die. The eggs hatch into larvae which eat and grow and then in the winter they fall in a pupal stage. The adults appear from the pupae in spring. Moreover, discrete models can present much more dynamical behaviors compared to the continuous-time model. 

This book consists of four chapters: 

  • Chapter 1: An Approach to Local Stability Analysis and Bifurcations of a Discrete-Time Host-Parasitoid Model
  • Chapter 2: An Overview of Chaos Induced by Snap-Back Repeller in a Two Species Competitive Model
  • Chapter 3: Application of Population Dynamics in Chaos Synchronization in Discrete-Time Dynamical Systems
  • Chapter 4: An Investigation on Synchronized Cycles of Generalized Nicholson-Bailey Model

Chapters

  • Chapter 1
    An Approach to Local Stability Analysis and Bifurcations of a Discrete-Time Host-Parasitoid Model
    Tahmineh Azizi
  • Chapter 2
    An Overview of Chaos Induced by Snap-Back Repeller in a Two Species Competitive Model
    Tahmineh Azizi, Bacim Alali
  • Chapter 3
    Application of Population Dynamics in Chaos Synchronization in Discrete-Time Dynamical Systems
    Tahmineh Azizi, Gabriel Kerr
  • Chapter 4
    An Investigation on Synchronized Cycles of Generalized Nicholson-Bailey Model
    Tahmineh Azizi, Gabriel Kerr
Cover for Discrete Dynamical Systems: With Applications in Biology
Published
September 8, 2020

Details about the available publication format: Purchase Book

ISBN-13 (15)
978-81-947204-4-7

Details about the available publication format: PDF

ISBN-13 (15)
978-81-947204-3-0

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