Subventions et des contributions :

Subvention ou bourse octroyée s'appliquant à plus d'un exercice financier. (2017-2018 à 2022-2023)

A distinguishing feature of the functional differential equations (FDEs) is that the evolution rate of the process described by such equations depends on the past history. During the past three decades, study on the theory and application of FDEs has been very active, the FDE related mathematical models are applicable to phenomena of different natures, such as, in biology, ecology, epidemiology, engineering and economy.

The long-term goals of the research include, understanding in-depth the dynamical behavior and the reasons that govern such behavior in biological and epidemiological systems that can be illustrated by FDEs, especially how time delay and the system structure affect the evolution of the species, whether the infectious disease can spread and persist, or lead to an infectious disease outbreak. Mathematical techniques based on nonlinear analysis, FDEs and dynamical systems including existence, non-existence, stability of certain type of periodic/quasi-periodic solutions, persistence, bifurcations will be mainly approached.

More realistic models may relate to the variation of environment which result in non-autonomous systems. In the literature, although some work has been done for autonomous and non-autonomous FDEs, there is a lack of theoretical analysis, especially for the stability and bifurcations. In the proposed research I will seek to extend and develop the stability and bifurcation theories to non-monotonic autonomous, non-autonomous, spatial and temporal involved FDEs with delays . And I will apply the theoretical results to tackle problems of qualitative analysis of dynamical behaviors arising in biological and epidemiological systems with stage/age-structures, or even disease transmission network models, with particular emphasis on establishing strong links on the effect of time delay, system construction and the dynamical behavior. I am also flexible enough to explore promising avenues of research as they emerge.

This proposed research will increase our knowledge of the qualitative properties in applied FDEs, from mathematical and biological/epidemiological points of view. The theories and methodologies developed in the proposal will have very high impact on the development in the nonlinear dynamics community. They will not only strengthen the foundation for theoretical expansion in a large class of FDEs, but will also provide a practical view to support biological and epidemiological decision making. The interdisciplinary collaboration and the application to the fishery will have great potential to provide novel insights to strength marine population dynamics, optimize harvesting rates, and maintain ecosystem structure. The anticipated outcomes are likely to have impact by leading to advancements in the field of applied dynamics and will enhance HQP training and collaboration benefiting in Canada.