Research

Publications

[3] D.D. Hai, D. Nichols, R. Shivaji. A uniqueness result for a p-Laplacian infinite semipositone problem with nonlinear boundary conditions. JMAA. July 2023. https://www.sciencedirect.com/science/article/pii/S0022247X23005140

[2] A. Acharya, V. Munoz, D. Nichols, R. Shivaji. An exact bifurcation diagram for a (p,q)-Laplacian boundary value problem. EJQTDE. January 2023. https://www.math.u-szeged.hu/ejqtde/p10056.pdf

[1] N. Fonseka, A. Henderson, J. Goddard II, D. Nichols, R. Shivaji. Modeling effects of matrix heterogeneity on population persistence at the patch-level. MBE. May 2022. https://www.aimspress.com/article/10.3934/mbe.2022638

10.3934_mbe.2022638 (3).pdf

p10056.pdf

1-s2.0-S0022247X23005140-main.pdf

Current Projects

10.3934_mbe.2020399 (3).pdf

In the literature, it has been established that trait mediated effects can sometimes have a more substantial impact on population persistence than direct, density-mediated effects.

In the paper A Review of Trait-Mediated Indirect Interactions in Ecological Communities by Werner and Peacor (2003), several examples of trait-mediated behavior are given. For instance, they cite the work of Beckerman et al (1997), Schmitz (1998), and Rothley (1997) who studied the interaction of spiders and grasshoppers in a field with different food types present for the grasshopper.

To isolate the trait effect (i.e. no predator-prey interaction) the spiders had their chelicerae (mouth parts) glued. It was found that grasshoppers reduced their activity and shifted their diet to include more herbs, even though no predation occurred.

In 2020, the authors Cronin, Goddard II, Muthunayake, and Shivaji published a paper where they studied a coupled, nonlinear model which examines cooperative effects of two species imposed through the boundary conditions. We are currently working to extend this paper in two additional directions: competition of two species and predator-prey.

Bifurcation diagrams (in the 1D case) provide us with an idea of where the regions of nonexistence and coexistence of positive solutions are and when multiplicity of positive solutions is possible.

The horizontal axis is related to the square of patch size and the vertical axis records the maximum density of the solution. We look for evidence of patch-level weak Allee effects and dead zones.