Kevin K Lin

Networks of Dynamical Systems

• Spike-time reliability of layered neural oscillator networks,
  with E. Shea-Brown and L.-S. Young,
  J. Comput. Neurosci. 27 (2009) pp. 135-160
  
  ( published version | preprint )

• Reliability of layered neural oscillator networks,
  with E. Shea-Brown and L.-S. Young,
  Commun. Math. Sci. 7 (2009) pp. 239-247
  
  ( preprint )

• Reliability of coupled oscillators,
  with E. Shea-Brown and L.-S. Young,
  J. Nonlin. Sci. 19 (2009) pp. 497-545
  
  ( Part I preprint | Part II preprint | published version )

• Reliable and unreliable dynamics in driven coupled oscillators,
  with E. Shea-Brown and L.-S. Young,
  arXiv:nlin/0608021v1 (2006)
  
  ( preprint )

• Propagating coalitions in networks of nonlinear oscillators,
  with F. Hoppensteadt,
  Sci. Math. Japon. 64 (2006) pp. 779-784

Dynamics of Neuron Models

• New! Limitations of perturbative techniques in the analysis of rhythms and oscillations,
  with K. C. A. Wedgwood, S. Coombes, and L.-S. Young
  to appear in J. Math. Biol.
  ( preprint )

• Entrainment and chaos in a pulse-driven Hodgkin-Huxley oscillator,
  SIAM J. Applied Dyn. Sys. 5 (2006) pp. 179-204
  
  ( published version | preprint )

Nonequilibrium Steady States

• Nonequilibrium steady states for certain Hamiltonian models,
  with L.-S. Young,
  J. Statist. Phys. 139 (2010) pp. 630-657
  
  ( published version | preprint )

• Ergodicity and energy distributions for some boundary driven integrable Hamiltonian chains,
  with P. Balint and L.-S. Young,
  Commun. Math. Phys. 294 (2010) pp. 199-228
  
  ( published version | preprint )

• Correlations in nonequilibrium steady states of random-halves models,
  with L.-S. Young,
  J. Statist. Phys. 128 (2007) pp. 607-639
  
  ( published version | preprint )

Numerical Methods

• Coming soon: Control Theory and Experimental Design in Diffusion Processes, in preparation

• Coupling control variates for Markov chain Monte Carlo,
  with J. Goodman,
  J. Comput. Phys. 228 (2009) pp. 7127-7136
  
  ( published version | preprint )

• Random perturbations of SRB measures and numerical studies of chaotic dynamics,
  PhD thesis in Mathematics, supervised by Alexandre Chorin
  LBL Technical Report 53522 (2003)
  
  ( abstract )

• Coordinate-independent computations on differential equations,
  MEng thesis in Computer Science and Engineering, supervised by Gerald Jay Sussman
  MIT AI Tech Memo 1631 (1997)
  
  ( abstract )

Shear-Induced Chaos

• Dynamics of periodically-kicked oscillators,
  with L.-S. Young
  Journal of Fixed Point Theory and Applications 7 (2010) pp. 291-312
  ( published version | preprint )

• Shear-induced chaos,
  with L.-S. Young,
  Nonlinearity 21 (2008) pp. 899-922 (a "high-profile article of 2008")
  
  ( published version | preprint )

Scaling Laws and Perturbations of Chaotic Systems

• Convergence of invariant densities in the small-noise limit,
  Nonlinearity 18 (2005) pp. 659-683
  
  ( published version | preprint )

• The Selberg zeta function for convex co-compact Schottky groups,
  with L. Guilllopé and M. Zworski,
  Commun. Math. Phys. 245 (2004) pp. 149-176
  
  ( published version | preprint )

• Numerical study of quantum resonances in chaotic scattering,
  J. Comput. Phys. 176 (2002) pp. 295-329
  
  ( published version | preprint )

• Quantum resonances in chaotic scattering,
  with M. Zworski,
  Chem. Phys. Lett. 355 (2002) pp. 201-205.
  
  ( published version | preprint )

The work described above have been supported by the National Science Foundation (under grant DMS-0907927 and a Mathematical Sciences Postdoctoral Fellowship), the Fannie and John Hertz Foundation, the LBL Math Department and NERSC, and Project MAC.

Collaborators: Peter Balint, Alexandre Chorin, Jonathan Goodman, Laurent Guilllopé, Frank Hoppensteadt, Eric Shea-Brown, Gerald Jay Sussman, Lai-Sang Young, and Maciej Zworski.