C1: Introduction to Delay Differential Equations with Applications
Speaker: Assoc. Prof. Dr. Juancho Collera
Abstract: This course is an introduction to delay differential equations (DDEs). The approach is rather intuitive and often pointing out the similarities and differences with ordinary differential equations (ODEs). The first half of the course will provide familiarity with the basic theories in DDEs including use of available software for solving systems of DDEs. The second half of the course focuses on some examples in theoretical ecology and will use the basic theories from the first half. We end by mentioning some related works and outlook.
C2: Recent Research in Dynamical System and Related Topics
Speaker: Prof. Dr. Salmi Md. Noorani
Abstract: This course will focus on some recent research in the fields of dynamical systems, ergodic theory, synchronisation and other related areas in mathematics. We will review these different topics of research and provide necessary details in term of their theoretical and computational backgrounds. We will also discuss some potential future work that can be further explored in these areas.
C3: Coupling Different Modelling Approaches in the Study of Competition Ecosystems
Speaker: Dr. Nguyen Ngoc Doanh
Abstract: This course focuses on coupling some existing modelling approaches, such as Equation-Based Modelling (EBM), Individual-Based Modelling (IBM) and Graph-Based Modelling (GBM), in order to investigate competition ecosystems which is the most popular systems in ecology. Each modelling approach has its own strengths and weaknesses. Coupling them allows us to promote their advantages and use them in effective ways. The coupling will therefore be able to provide deep understandings about dynamical behaviours of reference systems. This course consists of a series of lectures/tutorials/case studies working group.
C4: Dynamical Systems Analysis for Fractional Differential Equations
Speaker: Assoc. Prof. Dr. Doan Thai Son
Abstract: This course introduces some fundamental aspects of the qualitative theory of fractional differential equations including the existence and uniqueness of solutions, the Lyapunov spectrum, the linearized asymptotic stability/instability theory and the invariant manifold theory.
C5: Dynamics and Bifurcations in Lotka-Volterra Type Systems
Speaker: Dr. Kie Van Ivanky Saputra
Abstract: Interaction between populations and interactions of the populations with the environment are typically highly nonlinear. Thus, mathematical models become important tools to establish the factors underlying the temporal changes in the abundance of natural population. This short course is intended to give an introduction to the mathematical analysis of Lotka-Volterra population models. We will begin by studying in detail some examples of two species models, before moving on to general population models for the interactions of n species. In the latter part, we will study systems of differential equations of Rn of the form where ei serves as a constant term. We will employ bifurcation analysis to analyse such system.