Yun Kang
Applied Sciences and Mathematics
College of Technology & Innovation
Arizona State University
7001 E. Williams Field Road,
Mesa, AZ 85212, USA

Office: Wanner Hall 340C
Email: yun.kang@asu.edu
Phone number: 480-727-5004

Area of research: Dynamical system
theory and Mathematical biology
Curriculum Vitae
My greatest achievement in 2008




Research Focus

    My main areas of study are Dynamical Systems and Mathematical Biology. My research interests have both theoretical and modeling components. The theoretical component is to study global dynamics of systems that are of interest to biologists, which includes permanence of population models, spatial patterns of invasive species with Allee effects in heterogenous environment, the role of space in the exploitation of resources. The modeling component is to explore different modeling techniques, based on experiments or important hypotheses, to get a better understanding of quantitatively and qualitatively various aspects of biological behaviors, structures, and processes.

Current Research Projects

    My current research projects involve the following topics:

      (1) Coexistence of interacting species in food web: For deterministic models, the idea of permanent coexistence, which guarantees convergence to an interior attractor from any strictly positive initial conditions, is regarded as a strong form of coexistence. Permanence, however, has not been widely used in discrete-time ecological models due to its complicated boundary attractors (e.g., the standard quadratic map). To ameliorate this problem, we apply the relative nonlinearity concept to give an easy-to-check criterion to imply permanence for general multiple-species-interacting discrete time population models. The work on two-species-interacting discrete time population models has been done with Peter Chesson, which can be extended to general n-species models.

      (2) The traditional concept of permanence, which would fail due to exceptional behavior on sets of measure zero is unlikely to be broadly useful, because the noise in nature implies that the system would not stay in such sets. For this reason, the concept of permanence needs to be generalized to exclude sets of measure zero. Currently, we (with Hal Smith) work on a simple competition model to show the concept of relative permanence.

      (3) Spatial pattern and the spreading of the invasive species with Allee effects. When an alien species invades a new area, the success of its expansion and the rate of its spread are determined by interplay among dispersal, population growth, interactions with other species and environmental heterogeneity. We develop two-patch models and integral-difference models to investigate how factors mentioned above affect pattern formation and the spreading of invasive species when it suffers Allee-effects.

      (4) Mathematical modeling on mutualistic symbiosis: Mutualistic symbiosis is a type of mutualism in which individuals interact physically, or even live within the body of the other mutualist. Frequently, the relationship is essential for the survival of at least one member. In general, there are three types of mutualistic symbiosis: facultative and obligate mutualisms. Facultative mutualisms are not essential for the survival of either species. Individuals of each species engage in mutualism when the other species is present. Obligate mutualisms are esstential for the survivial of one or both species.

      • Facultative Mutualisim: Mycorrhizal fungi form symbiotic associations with roots of plants that benefit plants primarily by improving uptake of soil nutrients and increasing stress tolerance. Most plants are colonized by one functional type of mycorrhizal fungi, but some plants such as the important riparian tree Populus fremontii (cottonwood) are colonized by 3 different functional fungal groups; ectomycorrhizal (EM), arbuscular mycorrhizal (AM) and dark septate endophyte fungi (DSE) each contributing different benefits. Shifts in colonization patterns are known to occur and various factors such as life stage and environmental variables. Our current ongoing project (with Jean Stutz) is to develop a mathematical model to examine these fungal colonization patterns over time in heterogenous enviornment.

      • Obligate Mutualisim: Leaf-cutting ants cannot eat leaves. Instead, they carry the cut pieces back to the nest and use it as compost to cultivate the fungus. The fungus cannot survive outside the nest or reproduce without the ants help. Here is an article that may give you a general view of the interaction between leave cutter ants and its fungus-ants. According to data, the division of labor is a very important factor that determines whether the cololy can survive at its early stage (one of the supporting evidences is the poster by Leah Drake, Rebecca Clark and Jennifer Fewell). We are developing a mathematical model to study the interaction between leaves cutter ants and fungus growth during early colony expansion, which is able to address the functional/numerical responses between ants and fungus, and the importance of the labor division at the early stage of colony expansion. This is an ongoing collaboration with Fewell Jennifer and her Ph.D student Clark Rebecca .

    Some Interesting Problems in Discrete Systems(Click here)