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Full-Text Articles in Non-linear Dynamics
Traveling Wave Solutions For Two Species Competitive Chemotaxis Systems, T. B. Issa, R. B. Salako, W. Shen
Traveling Wave Solutions For Two Species Competitive Chemotaxis Systems, T. B. Issa, R. B. Salako, W. Shen
Faculty Research, Scholarly, and Creative Activity
In this paper, we consider two species chemotaxis systems with Lotka–Volterra competition reaction terms. Under appropriate conditions on the parameters in such a system, we establish the existence of traveling wave solutions of the system connecting two spatially homogeneous equilibrium solutions with wave speed greater than some critical number c∗. We also show the non-existence of such traveling waves with speed less than some critical number c∗0 , which is independent of the chemotaxis. Moreover, under suitable hypotheses on the coefficients of the reaction terms, we obtain explicit range for the chemotaxis sensitivity coefficients ensuring c∗ = c∗0 , which …
Theoretical Investigation Of Intra- And Inter-Cellular Spatiotemporal Calcium Patterns In Microcirculation, Jaimit B. Parikh
Theoretical Investigation Of Intra- And Inter-Cellular Spatiotemporal Calcium Patterns In Microcirculation, Jaimit B. Parikh
FIU Electronic Theses and Dissertations
Microcirculatory vessels are lined by endothelial cells (ECs) which are surrounded by a single or multiple layer of smooth muscle cells (SMCs). Spontaneous and agonist induced spatiotemporal calcium (Ca2+) events are generated in ECs and SMCs, and regulated by complex bi-directional signaling between the two layers which ultimately determines the vessel tone. The contractile state of microcirculatory vessels is an important factor in the determination of vascular resistance, blood flow and blood pressure. This dissertation presents theoretical insights into some of the important and currently unresolved phenomena in microvascular tone regulation. Compartmental and continuum models of isolated EC …