Dynamical Systems, Bifurcation Analysis and Applications

1. Front Matter

   Pages i-x

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2. Ordinary Differential Equations

   1. Front Matter

      Pages 1-1

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   2. Mathematical Modeling and Stability Analysis of Population Dynamics

      • Auni Aslah Mat Daud

      Pages 3-13

   3. Optimal Harvesting Regions of a Polluted Predator-Prey Fishery System

      • Tau Keong Ang, Hamizah M. Safuan, Ummu Atiqah M. Roslan, Mohd Hafiz Mohd

      Pages 15-29

   4. Dynamics and Bifurcations in a Dynamical System of a Predator-Prey Type with Nonmonotonic Response Function and Time-Periodic Variation

      • Johan M. Tuwankotta, Eric Harjanto, Livia Owen

      Pages 31-49

   5. Modeling and Experimental Data on the Dynamics of Predation of Rice Plants and Weeds by Golden Apple Snail (Pomacea Canaliculata)

      • Joel Addawe, Zenaida Baoanan, Rizavel Addawe

      Pages 51-65

3. Fractional Differential Equations

   1. Front Matter

      Pages 67-67

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   2. Analysis of a Discrete-Time Fractional Order SIR Epidemic Model for Childhood Diseases

      • Mahmoud A. M. Abdelaziz, Ahmad Izani Ismail, Farah A. Abdullah, Mohd Hafiz Mohd

      Pages 69-88

4. Delay and Partial Differential Equations

   1. Front Matter

      Pages 89-89

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   2. A Tuberculosis Epidemic Model with Latent and Treatment Period Time Delays

      • Jay Michael R. Macalalag, Elvira P. De Lara-Tuprio, Timothy Robin Y. Teng

      Pages 91-115

   3. Numerical Bifurcation and Stability Analyses of Partial Differential Equations with Applications to Competitive System in Ecology

      • Mohd Hafiz Mohd

      Pages 117-132

5. Discrete Dynamical Systems

   1. Front Matter

      Pages 133-133

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   2. Global Stability Index for an Attractor with Riddled Basin in a Two-Species Competition System

      • Ummu Atiqah Mohd Roslan, Mohd Tirmizi Mohd Lutfi

      Pages 135-146

   3. Counting Closed Orbits in Discrete Dynamical Systems

      • Azmeer Nordin, Mohd Salmi Md Noorani, Syahida Che Dzul-Kifli

      Pages 147-171

6. Computational Dynamical Systems

   1. Front Matter

      Pages 173-173

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   2. Computational Dynamical Systems Using XPPAUT

      • Ojonubah James Omaiye, Mohd Hafiz Mohd

      Pages 175-203

   3. A Basic Manual for AUTO-07p in Computing Bifurcation Diagrams of a Predator-Prey Model

      • Livia Owen, Eric Harjanto

      Pages 205-224

   4. Numerical Continuation and Bifurcation Analysis in a Harvested Predator-Prey Model with Time Delay using DDE-Biftool

      • Juancho A. Collera

      Pages 225-241

This book is the result of ​Southeast Asian Mathematical Society (SEAMS) School 2018 on Dynamical Systems and Bifurcation Analysis (DySBA). It addresses the latest developments in the field of dynamical systems, and highlights the importance of numerical continuation studies in tracking both stable and unstable steady states and bifurcation points to gain better understanding of the dynamics of the systems. 

The SEAMS School 2018 on DySBA was held in Penang from 6th to 13th August at the School of Mathematical Sciences, Universiti Sains Malaysia.The SEAMS Schools are part of series of intensive study programs that aim to provide opportunities for an advanced learning experience in mathematics via planned lectures, contributed talks, and hands-on workshop.

This book will appeal to those postgraduates, lecturers and researchers working in the field of dynamical systems and their applications. Senior undergraduates in Mathematics will also find it useful.

• dynamical systems
• bifurcation
• population dynamics
• disease resistance
• dispersal models
• riddled basin
• predator-prey system
• competition ecosystems
• XPPAUT/Auto

• School of Mathematical Sciences, Universiti Sains Malaysia, USM, Penang, Malaysia

  Mohd Hafiz Mohd, Norazrizal Aswad Abdul Rahman, Nur Nadiah Abd Hamid, Yazariah Mohd Yatim

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