CT1: Dynamical Systems in Agriculture: A Case Study on Plant Disease Resistance
Speaker: Dr. Nurul Syaza Abdul Latif
Abstract: The spread of an epidemic is often modelled with SIR (susceptible-infected recovered) system of equations. Can we modify this model to describe the SIR compartments for plant disease resistance? This is crucial to have a better understanding the dynamics of the phenomenon in a given plant cohort against a selected disease-causing pathogen. In this talk, a mathematical model of plant disease resistance promoted by chemical elicitor is described. The phase plane of this dynamical system predicts the relative proportion of plants in each compartment and quantitatively estimates elicitor effectiveness.
CT2: Dynamical Systems Analysis of Local and Non-Local Dispersal Models
Speaker: Dr. Mohd Hafiz Mohd
Abstract: In this talk, we discuss the effects of different dispersal patterns on the occurrence of priority effects (alternative stable states) and coexistence in multi-species communities by employing local (partial-differential equations) and non-local dispersal (integro-differential equations) models. Our analysis shows the existence of a threshold value in dispersal strength (i.e. saddle-node bifurcation) above which priority effects disappear. These results also reveal a co-dimension 2 point, corresponding to a degenerate transcritical bifurcation: at this point, the transcritical bifurcation changes from subcritical to supercritical with the corresponding creation of a saddle-node bifurcation curve.
CT3: Fish Population Dynamics with Harvesting and Toxicant Effects
Speaker: Dr. Hamizah Mohd Safuan
Abstract: This study discusses fish population dynamics when subjected to harvesting and toxicant effects. Poor harvesting strategies such as overfishing/overharvesting lead to an extinction of certain species of fish from the environment. Besides overfishing, toxic substances also contribute to the harmful effects on the fish population. This study considered fishery models that involve population interactions such as predation and competition with harvesting and toxicant terms. The equilibria of the model were obtained and the simulations of the bifurcation diagrams were performed to investigate the dynamical behaviours of the fish population.
CT4: Mathematical Modeling and Stability Analysis of Population Dynamics
Speaker: Dr. Auni Aslah Mat Daud
Abstract: This talk is intended to serve as an introduction to the formulation, analysis and application of mathematical models that describe the population dynamics. In the session, we will provide a brief discussion on the definition of important terminologies and concepts in the mathematical modelling and stability analysis of the population dynamics, the aims and significance of the study and the methodologies employed in the research. Several current, existing real-world applications will be presented. A simple example of such application will be discussed in detail as a case study. The computation and numerical simulation using MATLAB will be used in the modelling and stability analysis.
CT5: Stability Index for the Characterization of Riddled Basin in a Coupled Dynamical System
Speaker: Dr. Ummu Atiqah Mohd Roslan
Abstract: We consider a coupled dynamical system with a Milnor attractor whose basin of attraction is riddled with the basin of a second attractor. We first study how the global geometry of the basin of attraction changes as we vary the parameter in the system. Secondly, we focus on the local geometry of the riddled basin of attraction. To characterize this riddled basin, we compute a stability index for the attractor in the system. Our numerical results show that for Lebesgue almost all points in the attractor, the index is positive for some parameter region where the riddled basin occurs.