• Gene Regulatory Networks

• E. Boczko, T. Cooper, T. Gedeon, K. Mischaikow, D. Murdock, S. Pratap, and S. Wells, Structure Theorems and the Dynamics of Nitrogen Catabolite Repression in Yeast

• Population Biology

• M. Grinfeld, G. Hines, V. Hutson, K. Mischaikow, and G. Vickers, Nonlocal Dispersal,
• S. Day, O. Junge, and K. Mischaikow, A Rigorous Numerical Method for the Global Analysis of Infinite Dimensional Discrete Dynamical Systems  (To appear in SIAM Dynamical Systems).
• V. Hutson, S. Martinez, K. Mischaikow, and G. T. Vickers, The evolution of dispersal. J. Math Biology 47 (2003) 483--517.
• V. Hutson, Y. Lou,  K. Mischaikow, and P. Polacik,  Competing Species Near a Degenerate Limit (The final version can be found in SIAM Math Anal. 35 (2003) 453--491)
• V. Hutson, Y. Lou, and K. Mischaikow,  Spatial Heterogeneity of Resources versus Lotka-Volterra Dynamics, (The final version can be found in J. Diff. Eqns. 185 (2002))
• V. Hutson, K. Mischaikow, and P. Polacik,  The Evolution of Dispersal Rates in a Heterogeneous Time-Periodic Environment  (The final version can be found in J Math Biol 43 (2001) 6, 501-533)
• V. Hutson, K. Mischaikow, and G. T. Vickers, Multiple Travelling Waves in Evolutionary Game Dynamics (The final version can be found in Japanese Journal of Industrial and Applied Math.)
• V. Hutson and K. Mischaikow, Periodic Travelling Waves . (The final version can be found in Conley Index Theory, Banach Center Publications, 47, 1999.)
• J. Dockery, V. Hutson, K. Mischaikow, M. Pernarowski , The evolution of slow dispersal rates: a reaction diffusion model (The final version can be found in J. Math. Biol. 37 (1998) 61-83 )

Computational Homology

• Theory

• K. Mischaikow, M. Mrozek , P. Pilarczyk ,  Graph Approach to the Computation of the Homology of Continuous Maps
• T. Kaczynski, K. Mischaikow and M. Mrozek , Computing Homology  (The final version can be found at  Homology, Homotopy and Applications 5 (233-256) 
  
• W. Kalies, K. Mischaikow, and G. Watson, Cubical Approximation and Computation of Homology   (The final version can be found in Conley Index Theory, Banach Center Publications, 47, 1999.)

• Applications

• M. Gameiro,  K. Mischaikow and T. Wanner, Evolution of Pattern Complexity in the Cahn-Hilliard Theory of Phase Separation
• M. Gameiro, W. D. Kalies, and K. Mischaikow, Topological Characterization of Spatial Temporal Chaos,
• M. Niethammer, A. N. Stein, W. D. Kalies,  P. Pilarczyk, K. Mischaikow, A. Tannenbaum,   Analysis of Blood Vessel Topology by Cubical Homology
  
• M. Allili, K. Mischaikow, A. Tannenbaum,  Cubical homology and the topological classification of 2D and 3D imagery, IEEE International Conference on Image Processing, v 2, 2001, p 173-176

Computational Dynamics

• Theory

• K. Mischaikow, Topological Techniques for Efficient Rigorous Computations in Dynamics  (pdf)  (The final version can be found in Acta Numerica 2002.)
• K. Mischaikow and M. Mrozek , Conley Index Theory

• Low Dimensional Dynamics

• Z. Arai and K. Mischaikow, Rigorous Computations of Homoclinic Tangencies
• S. Day, O. Junge, and K. Mischaikow, Towards Automated Chaos Verification, (To appear in Proc. Equadiff 2003)
• K. Mischaikow, M. Mrozek , and A. Szymczak ,  Chaos in the Lorenz equations: A computer assisted proof. Part III: Classical Case Parameter Values
• K. Mischaikow and M. Mrozek , Chaos in the Lorenz equations: A computer assisted proof. Part II: Details (The final version can be found in Mathematics of Computation, 67 (1998) 1023-1046)

• Infinite Dimensional Dynamics

• S. Day, Y. Hiraoka, K. Mischaikow, and T. Ogawa, Rigorous Numerics for Global Dynamics: a study of the Swift-Hohenberg equation,
  
• S. Day, O. Junge, and K. Mischaikow, A Rigorous Numerical Method for the Global Analysis of Infinite Dimensional Discrete Dynamical Systems  (To appear in SIAM Dynamical Systems).
• P. Zgliczynski  and K. Mischaikow,  Rigorous Numerics for Partial Differential Equations: the Kuramoto-Sivashinsky equation   (The final version can be found in Foundations of Comp. Math. 1 255-288.)

Conley Index

• Theory

• T. Gedeon, H. Kokubu, K. Mischaikow, and H. Oka, The Conley index for fast-slow systems II: Multi-dimensional slow variable,   
• K. Mischaikow and M. Mrozek , Conley Index Theory
• K. Mischaikow, M. Mrozek , A. Szymczak , and J. Reiss , From Time Series to Symbolic Dynamics: An Algebraic Topological Approach (preliminary version)
• H. Kokubu, K. Mischaikow, and H. Oka, Directional Transition Matrix.  (The final version can be found in Conley Index Theory, Banach Center Publications, 47, 1999.)
• Maria C. Carbinatto, and K. Mischaikow, Horseshoes and the Conley Index Spectrum - II: The Theorem is Sharp (The final version can be found in Discrete and Continuous Dynamical Systems,5 (1999) 599-616)
•  T. Gedeon, H. Kokubu, K. Mischaikow, H. Oka, and J. Reineck, The Conley index for fast-slow systems I: One dimensional slow variables. (The final version can be found in Jour. Dyn. Diff. Eqs., 11 (1999) 427-470)
• K. Mischaikow, M. Mrozek, and J. Reineck, Singular Index Pairs (The final version can be found in Jour. Dyn. Diff. Eqs., 11 (1999) 399-425)
• Maria C. Carbinatto, Jarek Kwapisz, and K. Mischaikow, Horseshoes and the Conley Index Spectrum (this is an update of the October 7, 1996 version)
• K. Mischaikow, The Conley Index Theory: A Brief Introduction .  (The final version can be found in Conley Index Theory, Banach Center Publications, 47, 1999.)

• Applications

• T. Gedeon , H. Kokubu, K. Mischaikow, and H. Oka,  Chaotic solutions in slowly varying perturbations of Hamiltonian systems with applications to shallow water sloshing (The final version can be found in Journal of Dynamics and Differential Equations).
• K. Mischaikow, M. Mrozek, J. Reiss and A. Szymczak, Construction of Symbolic Dynamics from Experimental Time Series (The final version can be found in Physical Review Letters Vol. 82, No. 6 page 1144, February 1999).
• V. Hutson and K. Mischaikow, Periodic Travelling Waves . (The final version can be found in Conley Index Theory, Banach Center Publications, 47, 1999.)
• Hiroshi Kokubu, K. Mischaikow, Yasumasa Nishiura, Hiroe Oka, and Takeshi Takaishi, Connecting orbit structure of monotone solutions in the shadow system (the final version can be found in JDE, vol. 140 (1997) 309-364).

Computer Graphics

• Eugene Zhang, K. Mischaikow, G. Turk, Feature Based Surface Parameterization and Texture Mapping,

Konstantin Mischaikow
Center for Dynamical Systems and Nonlinear Studies
School of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332-0190
USA

Send mail to me at mischaik@math.gatech.edu
Phone: (404) 894-4749
FAX: (404) 894-1726

Last Modified on July 14, 2004

Disclaimer:
The contents of this page reflect solely the opinions of the author who originated it. It has not been reviewed by, nor is it a publication of the Georgia Institute of Technology.