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