Math Ecology

My research interests lie in the fields of mathematical control theory, mathematical ecology, and connections between the two.

Below are some of my publications in mathematical ecology:

• Global asymptotic stability of density dependent integral population projection models, R. Rebarber, B. Tenhumberg and S. Townley, Theoretical Population Biology, 81 (2012) 81-87
• Choice of density dependent seedling recruitment function affects predicted transient dynamics: A case study with Platte thistle, Eric Alan Eager, Richard Rebarber and Brigitte Tenhumberg, to appear in Theoretical Ecology
• Feedback control systems analysis of density dependent population dynamics, S. Townley, B. Tenhumberg and R. Rebarber, Systems & Control Letters, 61 (2012) 309-315.
• The effects of belowground resources on aboveground allometric growth in Bornean tree species, Katherine D. Heineman, Ethan Jensen, Autumn Shapland, Brett Bogenrief, Sylvester Tan, Richard Rebarber and Sabrina E. Russo, Forest Ecology and Management, 261 (2011) pp. 1820-1832.
• Structured Population Dynamics and Calculus: An Introduction to Integral Modeling, by J. Briggs, K. Dabbs, M. Holm, J. Lubben, R. Rebarber, D. Riser-Espinoza and B. Tenhumberg, Mathematics Magazine 83: 4 (2010), pp. 243-257.
• Parameterizing the growth-decline boundary for uncertain population projection models, by J. Lubben, D. Boeckner, R. Rebarber, S. Townley and B. Tenhumberg, Theoretical Population Biology, 75(2009), pp. 85-97.
• Model complexity affects predicted transient population dynamics following a dispersal event: A case study with Acyrthosiphon pisum, by B. Tenhumberg, A. Tyre and Richard Rebarber, Ecology 90, 7(2009), 1878-1890.
• Management recommendations based on matrix projection models: the importance of considering biological limits, by J. Lubben, B. Tenhumberg, A. Tyre and R. Rebarber, Biological Conservation, 141, 2 (2008) pp. 517-523.
• Robust population management under uncertainty for structured population models, by A. Diences, E. Peterson, D. Boeckner, J. Boyle, A. Keighley, J. Kogut, J. Lubben, R. Rebarber, R. Ryan, B. Tenhumberg, S. Townley and A. Tyre, Ecological Applications, 17 (2007), pp. 2175-2183.

Below are some of my publications in distributed parameter control theory:

• Invariant Zeros of SISO Infinite-Dimensional Systems, by K. Morris and R. Rebarber, Interna- tional Journal of Control, 83, no. 12 (2010), pp. 2573-2579.
• A sampled-data servomechanism for stable well-posed systems, by Z. Ke, H. Logemann, and R. Rebarber, IEEE Trans. Automatic Control, 54, 5(2009), pp. 1123-1128.
• Approximate tracking and disturbance rejection for stable infinite-dimensional systems using sampled-data low-gain control, by Z. Ke, H. Logemann, and R. Rebarber, SIAM J. Control Optimization, 48, 2(2009), pp. 641-671.
• Feedback Invariance of SISO infinite-dimensional systems, by K. Morris and R. Rebarber, Mathematics of Control, Signals and Systems, 19 (2007), pp. 313-335.
• Robustness with Respect to Sampling for Stabilization of Riesz Spectral Systems, by R. Rebarber and S. Townley, IEEE Trans. Automatic Control, 51, 9 (2006), pp. 1519-1522.
• Generalized sampled-data stabilization of well-posed linear infinite-dimensional systems, by Hartmut Logemann, Richard Rebarber and Stuart Townley, SIAM J. Control and Optimization, 44, No. 4 (2005), pp. 1345-1369.
• Stability of Infinite Dimensional Sampled Data Systems, by Hartmut Logemann, Richard Rebarber and Stuart Townley, Transactions of the American Mathematical Society, 355, No. 8 (2003), pp. 3301-3328.
• Internal Model Based Tracking and Disturbance Rejection for Stable Well-Posed Systems, by Richard Rebarber and George Weiss, Automatica, 39, (2003), pp. 1555-1569.
• Boundary Controllability of a Coupled Wave/Kirchoff System, by George Avalos, Irena Lasiecka and Richard Rebarber, Systems & Control Letters, 50, (2003), pp. 331-341.
• Non-Robustness of Closed-Loop Stability for Infinite Dimensional Systems Under Sample-and-Hold, by Richard Rebarber and Stuart Townley, IEEE Transactions on Automatic Control, 47 (8), (2002) pp. 1381-1385.