Anatoli Ivanov

Professor, Mathematics
Office Phone
Office Location
Science Center, Room 108C
Monday/Wednesday/Friday, 12:00–13:00
Penn State Wilkes-Barre
44 University Drive
Dallas, PA 18612
Biography

I am currently Professor of Mathematics at the Pennsylvania State University, USA (since 1994). Since earning my Ph.D. in 1983 I have been employed, held a long-term visiting position or a Fellowship at numerous academic institutions around the world, including Institute of Mathematics, Ukrainian Academy of Sciences, Kiev, Ukraine; Institute of Mathematics, University of Munich and Institute of Mathematics, University of Giessen, Germany; University of Rhode Island, Georgia Institute of Technology, and University of Minnesota, Minneapolis, USA; Deakin University, Melbourne, and University of Ballarat, Australia; University of Chile, Santiago, and University of Talca, Chile; University of Vigo, Spain.

Education

I graduated from Kiev State University, Faculty of Mathematics, in 1978 and received an Honors Degree. I studied mathematics with emphasis on dynamical systems, differential and functional differential equations, and interval maps. My Diploma Thesis (M.Sc.) was entitled “Periodic Solutions of Systems of Differential Equations with Switching.” During 1980-83, I was a graduate student at the Institute of Mathematics of the Ukrainian Academy of Sciences (Kiev, Ukraine). In 1983 I successfully defended my Candidate Dissertation (Ph.D. thesis), entitled “Oscillations in First Order Functional Differential Equations,” earning the degree of Candidate of Physical and Mathematical Sciences. My Ph.D. adviser was Professor A.N. Sharkovsky.

Honors, Awards, and Fellowships

In 1988 I was awarded the “Prize with Medal for Young Scientists” of the Ukrainian Academy of Sciences for a series of publications on interval maps and their applications (shared with my colleague Dr. V.V. Fedorenko). This is a national prize with only one award in mathematics.

I was awarded research fellowships by the Japan Society for the Promotion of Science in 1985, 1997 and 1998 (Japan), the Alexander von Humboldt Fellowships in 1990, 1998, 2001, 2004, and 2010 (Germany), and the Fulbright Fellowship in 2002 (USA) for a research/teaching project in Chile.

Teaching Experience

My teaching career spans over 25 years and includes extensive and various pedagogical experience in a number of countries such as Ukraine/USSR, Australia, and the United States. I have taught practically every mathematics course in the undergraduate curriculum. In addition, I have taught a number of the graduate level courses which deal with various aspects in dynamical systems and differential equations, including applications of functional differential equations in modeling of real-life phenomena. I have been teaching at the Pennsylvania State University since 1994. With every regular course in mathematics I usually offer the Honors Option for that course, which assumes the in-depth and expanded study of the subject. In addition I have offered and supervised a number of student research projects.

Research Interests

My research interests are in differential equations (ordinary, delay, functional), dynamical systems, difference equations, bifurcation theory, and chaotic systems. I am particularly interested in applications of these to engineering, biological, and economics problems. (AMS Subject Classification: 34K, 37E, and 39A)

My recent work has been concerned with the asymptotic behavior of solutions of differential delay equations, including the existence and stability of periodic solutions and chaotic behavior, optimization and control in functional differential equations, as well as with one-dimensional dynamical systems.

I frequently collaborate with people whose specialties lie outside my own. I find collaboration, in general, to be a fruitful and enriching process. Currently I have active collaborative ties and joint ongoing research projects with several research groups around the world. They include:

• University of Talca, Chile (Prof. S. Trofimchuk)

• CIAO, University of Ballarat (Drs. M. Mammadov and Z. Dzalilov)

• Kiev National University, Ukraine (Profs. D. Khusainov and I. Dzhalladova)

• University of Giessen, Germany (Prof. Dr. H.-O. Walther and Prof. Dr. B. Lani-Wayda)

• Shimane University, Japan (Prof. T. Furumochi)

• University of Calgary, Canada (Prof. A. Swishchuk)

• University of Vigo, Spain (Prof. E. Liz)

Publications

A.F. Ivanov, C. Gomez, and S.I. Trofimchuk, On the existence of non-monotone non-oscillating wavefronts. Journal of Mathematical Analysis and Applications 419 (2014), 606-616.

A.F. Ivanov, M.A. Mammadov, and S.I. Trofimchuk, Global stabilization in nonlinear discrete systems with time-delay. Journal of Global Optimization 56 (2013), 251-263.

A.F. Ivanov and S.I. Trofimchuk, Periodic solutions of a discretized differential delay equation. Journal of Difference Equations and Applications 16, nos. 2-3 (2010), 157-171.

A.F. Ivanov and M.A. Mammadov, Global stability, periodic solutions, and optimal control in a nonlinear differential delay model. Electronic Journal of Differential Equations, Conf. 19 (2010), 177–188.

A.F. Ivanov, Global dynamics of a differential equation with piecewise constant argument. Nonlinear Analysis: Theory, Methods and Applications 71 (2009), e2384-e2389. (doi:10.1016/j.na.2009.05.030) (pdf-file)

A.F. Ivanov, On symmetric differential delay equations with cubic nonlinearity. Dynamic Systems and Applications 5 (2008), 227-233. (Proceedings of the 5th International Conference on Dynamic Systems and Applications)

A.F. Ivanov and A.V. Swishchuk, Optimal control of stochastic differential delay equations with application in economics. International Journal of Qualitative Theory of Differential Equations and Applications 2 (2008), 201-213.

A.F. Ivanov and S.I. Trofimchuk, Periodic solutions and their stability of a differential-difference equation. Discrete and Continuous Dynamical Systems – Supplement 2009, 385-393. Proceedings of 7th AIMS International Conference on Dynamical Systems and Differential Equations, UTA, May 17-21, 2008.

A.F. Ivanov and B. Lani-Wayda, Stability and instability criteria for Kaplan-York solutions. Zeitschrift fur angewandte Mathematik und Physik (ZAMP) 57 (2006), 1–29.

A. Ivanov and E. Liz, Periodic solutions of a singular differential delay equationwith the Farey-type nonlinearity. Journal of Computational and Applied Mathematics 180, no.1 (2005), 137-145.

A.F. Ivanov and B. Lani-Wayda, Periodic solutions for three-dimensional non-monotone cyclic systems with time delay. Discrete and Continuous Dynamical Systems 11 (2004), 667-692.

E. Liz, A. Ivanov, and J.B. Ferreiro, Discrete Halanay-type inequalities and applications. Nonlinear Analysis, TMA 55 (2003), 669-675.

P. Dormayer, A.F. Ivanov, and B. Lani-Wayda, Floquet multipliers of symmetric rapidly oscillating solutions of differential delay equations. Tohoku Mathematical Journal 54, No. 3 (2002), 419-441.

K.L. Cooke and A.F. Ivanov, On the discretization of a delay differential equation. Journal of Difference Equations and Applications 6, No. 1 (2000), 105-119.

A.F. Ivanov and J. Losson, Stable rapidly oscillating solutions in delay equations with negative feedback. Differential and Integral Equations 12 (1999), No. 6, 811-832.

P. Dormayer and A.F. Ivanov, Stability of symmetric periodic solutions with small amplitudes of x'(t)=af(x(t),x(t-1)). Discrete and Continuous Dynamical Systems 5 (1999), No.1, 61-82.

E.I. Verriest and A.F. Ivanov, Robust stability of systems with delayed feedback. Circuits, Systems, and Signal Processing 13 (1994), 213-222.

A.F. Ivanov, On global stability in a nonlinear discrete model. Nonlinear Analysis, Theory, Methods and Applications 23, no.11 (1994), 1383-1389.

J.K. Hale and A.F. Ivanov, On a high order differential delay equation. Journal of Mathematical Analysis and Applications 173 (1993), 505-514.

A.F. Ivanov, An example of infinitely many sinks for smooth interval maps. Acta Mathematica Universitatis Comenianae LXI, no.1 (1992), 3-9.

A.F. Ivanov and A.N. Sharkovsky, Oscillations in singularly perturbed delay equations. In: Dynamics Reported, New Series, Springer-Verlag 1 (1991), 164-224. (ed. by C.K.R.T. Jones, U. Kirchgraber, and H.-O. Walther).

A.N. Sharkovsky and A.F. Ivanov, Interval maps with attracting cycles of arbitrarily large periods. Ukrainian Math. J. 35, no.4 (1983), 537-539. (in Russian)

Education

Ph.D. in Physical and Mathematical Sciences, Institute of Mathematics of the Ukrainian Academy of Sciences (Kiev, Ukraine), 1983. Ph.D. adviser: Professor A.N. Sharkovsky. Thesis: “Oscillations in First Order Functional Differential Equations.”

M.Sc. in Mathematics with Honors, Kiev State University (U.S.S.R./Ukraine), 1978. Thesis: “Periodic Solutions of Systems of Differential Equations with Switching.”