Over the past eighteen years I have developed an interdisciplinary undergraduate and graduate research program in Applied and Computational Mathematics. The work has an emphasis on combining dynamical systems theory, group theoretical methods, i.e., equivariant bifurcation theory and representation theory, and computational methods to model, analyze, and predict the behavior of Complex Nonlinea...

We provide a local saddle-node bifurcation result for quasiperiodically forced interval maps. As an application, we give a rigorous description of saddle-node bifurcations of 3-periodic graphs in the quasiperiodically forced logistic map with small forcing amplitude. 2000 Mathematics Subject Classification.

Background and Objective: Cerebral Arteriovenous Malformation (CAVM) hemodynamic is disease condition, results changes in the flow and pressure level in cerebral blood vessels. Measuring flow and pressure without catheter intervention along the vessel is big challenge due to vessel bifurcations/complex bifurcations in Arteriovenous Malformation patients. The vessel geometry in CAVM patients are...

We consider the existence of limit cycles for a predator-prey system with a functional response. The system has two or more parameters that represent the intrinsic rate of the predator population. A necessary and sufficient condition for the uniqueness of limit cycles in this system is presented. Such result will usually lead to a bifurcation curve. 2000 Mathematics Subject Classification. 92D40.

We consider the static and dynamic models of Cournot duopoly with tax evasion. In the dynamic model we introduce the time delay and we analyze the local stability of the stationary state. There is a critical value of the delay when the Hopf bifurcation occurs. Mathematics Subject Classification: 34K18, 47N10; Jel Classification: C61, C62, H26

background and objective: cerebral arteriovenous malformation (cavm) hemodynamic is disease condition, results changes in the flow and pressure level in cerebral blood vessels. measuring flow and pressure without catheter intervention along the vessel is big challenge due to vessel bifurcations/complex bifurcations in arteriovenous malformation patients. the vessel geometry in cavm patients are...

As a kind of dynamical system with particular nonlinear structure, multi-time scale is one the essential directions current development dynamics theory. Multi-time systems in practical applications are often complex forms coupling high-dimensional and high codimension characteristics, leading to various bursting oscillation behaviors bifurcation characteristics system. For exploring caused by b...

We study the existence, stability, and dynamics of symmetric and anti-symmetric states of quasi-one-dimensional polariton condensates in doublewell potentials, in the presence of nonresonant pumping and nonlinear damping. Some prototypical features of the system, such as the bifurcation of asymmetric solutions, are similar to the Hamiltonian analog of the double-well system considered in the re...

A more realistic mathematical influenza model including dynamics of Twitter, which may reduce and increase the spread of influenza, is introduced. The basic reproductive number is derived and the stability of the steady states is proved. The existence of Hopf bifurcation are also demonstrated by analyzing the associated characteristic equation. Furthermore, numerical simulations and sensitivity...