Richard H. Rand
535 Malott Hall
207 Kimball Hall
Sc.D. (1967) Columbia University
Research Area
Nonlinear dynamics
My research involves using perturbation methods and bifurcation theory to obtain approximate solutions to differential equations arising from nonlinear dynamics problems in engineering and biology. Current projects involve differential equations which include delay terms and fractional derivatives. Applications include MEMS (micro electrical mechanical systems), dynamics of microbubbles, evolutionary dynamics, coupled oscillators and celestial mechanics. These projects are conducted jointly with graduate students and with experts in the respective application area.
Selected Publications
Using delay to quench undesirable vibrations (with M. K. Suchorsky and S. M. Sah), Nonlinear Dynamics 62 (2010), 407–416.
Fractional Mathieu equation (with S. M. Sah and M. K. Suchorsky), Communications in Nonlinear Science and Numerical Simulation 15 (2010), 3254–3262.
Dynamics of a model of two delay-coupled relaxation oscillators (with R. E. Ruelas), Communications in Nonlinear Science and Numerical Simulation 15 (2010), 1980–1988.
Dynamics of microbubble oscillators with delay coupling (with C. R. Heckman and S. M. Sah), Communications in Nonlinear Science and Numerical Simulation 15 (2010), 2735–2743.
Differential-delay equations; in Complex Systems: Fractionality, Time-Delay and Synchronization, chapter 3 (A. C. J. Luo and J-Q Sun, eds.), Springer, 2011, pp. 83–117.
Evolutionary dynamics of a system with periodic coefficients (with M. Yazhbin and D. G. Rand), Communications in Nonlinear Science and Numerical Simulation 16 (2011), 3887–3895.
Dynamics of three coupled limit cycle oscillators with vastly different frequencies (with H. Sheheitli), Nonlinear Dynamics 64 (2011), 131–145.
A digital model of coupled oscillators (with R.E. Ruelas), Communications in Nonlinear Science and Numerical Simulation 16 (2011), 1135–1139.
Center manifold reduction of the Hopf-Hopf bifurcation in a time-delay system (with C. Heckman), Journal of Applied Nonlinear Dynamics 1 (2012), 159–171.
On the dynamics of a thin elastica (with H. Sheheitli), International J. Nonlinear Mechanics 47 (2012), 99–107.
Nonlinear parametric excitation of an evolutionary dynamical system (with R. E. Ruelas and D. G. Rand), J. Mechanical Engineering Science 226 (2012), 1912–1920.
A pair of van der Pol oscillators coupled by fractional derivatives (with M. K. Suchorsky), Nonlinear Dynamics 69 (2012), 313–324.
Lecture Notes on Nonlinear Vibrations, Internet-First University Press, 2012.