UAH > Math > Faculty > Huang

Dr. Wenzhang Huang

Professor

Address Information

• Office: 334 Madison Hall
• Voice: (256) 824-2224
• Fax: (256) 824-6173
• E-Mail: huang@math.uah.edu

Research Interests:

• differential equations (including ordinary, partial, and functional differential equations)
• dynamical systems
• bifurcation
• singular perturbation
• population dynamics
• mathematical biology.

Current Research Project: Transition Layers and Connecting Orbits for a Class of Singularly Perturbed Systems of Differential-Difference Equations

Many biological and physical systems exhibit multiple-time-scale phenomenon and time delayed feedback. These typically occur in electrical circuits, nonlinear optics, biology, and physiology. Thus, the equations that describe the dynamics of such a system often form a time delayed, singularly perturbed system involving a small parameter. An important question is "what is the relation between the dynamics of the singularly perturbed system and the dynamics of its formal limit system (generated by letting the small parameter be zero)?" The specific interest of this project will be the investigation of the existence of a square wave like periodic solution when the limit system has a pair of period doubling points. The problem of the existence of a square wave periodic solution is not only important in applications, but is challenging to mathematicians. This problem has been studied intensively for scalar equations by many authors. In particular, very interesting results have been obtained by J. Mallet-Paret and R. Nussbuam. However the understanding of the underlying dynamics for higher dimensional systems is still in its infancy. The central part of this project is an attempt to develop a geometrical or global bifurcation method to study the existence of heteroclinic orbits to transition layer equations corresponding to the square wave periodic solution for a three dimensional system that is used as a model for a ring-cavity containing a nonlinear dielectric medium.

Selected Works

• " Monotonicity of Heteroclinic Orbits and Spectral Properties of Variational Equations for Delay Differential Equations," Journal of Differential Equations, 162 (2000), 91-139.
• "Competitive Exclusion and Coexistence of Multiple Strains in SIS STD Model," SIAM Journal on Applied Mathematics, 59 (1999), 1790-1811 (with Carlos Castillo-Chavez and Jia Li).
• "Global Dynamics for a Reaction-diffusion Equation with Time delay," Journal of Differential Equations, 143 (1998), 293-326.
• "Periodic Solution of Singular Perturbed Delay Equations," Zangew Mathematical Physics, 47 (1996), 57-88 (with Jack K. Hale).
• "On the Problems of Linearization for a Class of State-Dependent Functional Differential Equations," Proceedings of the American Mathematical Society, 124 ( 1996), 1417-1425 (with Kenneth Cooke).

Professional Background

• Ph.D. (math) Claremont Graduate School, 1990.
• M.S. (math) Anhui University, China, 1982.
• B.S. (fine arts) Fuyong Teachers College, China 1977.
• At UAH since 1994.