Selection of Publications

  1. The \v Sil'nikov problem, exponential expansion, strong $\lambda$-lemma, $C^1$-linearization, and homoclinic bifurcations, J.D.E., 79(1989), pp.189--231.
  2. Homoclinic bifurcations with nonhyperbolic equilibria, SIAM. J. Math. Anal., 21(1990), pp.693--719.
  3. The existence of infinitely many traveling front and back waves in FitzHugh-Nagumo equation, SIAM J. Math. Anal., 22(1991), pp.1631--1650.
  4. Smooth conjugacy of center manifolds (with A. Burchard and K.N. Lu), Proc. Royal Soc. Edinburgh, 120A(1992), pp.61--77.
  5. Homoclinic twisting bifurcations and cusp horseshoe maps, J.D.D.E., 5(1993), pp.417--467.
  6. Constructing homoclinic orbits and chaotic attractors, Int. J. Bif. & Chaos, 4(1994), pp.823--841.
  7. Constructing Lorenz type attractors through singular perturbations, Int. J. Bif & Chaos, 5(1995),  pp.1633-1642.
  8. Analytic conjugation, global attractor, and the Jacobian Conjecture, July 1995.
  9. Neural code renormalization, universal number 1, and super chaos, August 1997 -- October 2000. (Old title: ``A neuroencoding scheme and a new renormalization universality''. About neuroencoding, natural number 1 as a universal constant, and super chaos structure which contains all finite dynamical systems.)
  10. Glucose-induced period-doubling cascade in the electrical activity of pancreatic ß-cells, J. Math. Bio.,  38(1999), pp: 21 – 78.

Download Recent Preprints and Publications

  1. On a nonlinear communication scheme, with S.N. Chow and J.K. Hale, Int. J. Bif. & Chaos, 11(2001), pp.2227-2232. [PS]
  2. Theory and application of a nongeneric heteroclinic loop bifurcation, with S.N. Chow and M.J. Friedman, SIAM J. Appl. Math., 59(1999), pp.1303--1321.<!--[PDF]-->
  3. Chaotic attractors in one-dimension generated by a singular Shilnikov orbit, with K. Taylor, Int. J. Bif. and Chaos, 12(2001), pp.3059-3083. [PDF][PS]
  4. Singular perturbation of $n$-front traveling waves in the FitzHugh-Nagumo equations, with D. Bell, July 2001. [PDF][PS].
  5. Food chain chaos due to junction-fold point, Chaos, 11(2001), pp.514--525. [PDF][PS]
  6. Food chain chaos due to Shilnikov's orbit, with G. Hines, Chaos, 12(2002), pp.533--538. [PDF][PS]
  7. Food chain chaos due to transcritical point, with G. Hines, Chaos, 13(2003), pp.575--585. [PDF][PS]
  8. Outbreak-Crash Dynamics and Chaotic Interactions of Competition, Predation, Prolificacy in Specialist Food Webs, with B. Bockelman, E. Green, G. Hines, L. Lippitt, and J. Sherman, Feb. 2003. [PDF][PS]
  9. Biological control does not imply paradox---A case against ratio-dependent model, with Shannon Jessie, Glenn Ledder, Alex Rand, Sarah Srodulski, to appear in J. Mat. Bios. (2005). [PDF]
  10. Food chain chaos with canard point, Chaos, 14(2004), pp.1083—1092. [PDF][PDF]
  11. Chaotic Coexistence In A Top-Predator Mediated Competitive Exclusive Web, with B. Bockelman, E. Green, G. Hines, L. Lippitt, and J. Sherman, JDDE, 16(2004), pp.1062--1092. [PDF]
  12. Food web chaos without subchain oscillators, with B. Bockelman, (2005) [PDF][DOI]
  13. Why is the number of DNA bases 4? to appear in Bull. Math. Bio. (2005) (New!!!)[PDF] [DOI]
  14. Equilibriumizing All Food Chain Chaos, preprint, 2005 (New!!!)[PDF]
  15. Communication model of DNA replication, reprint (2006) (New!!!)[PDF]
  16. The Origin of 2 Sexes Through Optimization of Diversity Entropy Against Time and Energy, preprint (2006) (New!!!)[PDF]
  17. The Time Invariance Principle, Ecological (Non)Chaos, and A Fundamental Pitfall of Discrete Modeling, preprint (2006) (New!!!)[PDF]
  18. Mismatch Repair Error Implies Chargaff’s Second Parity Rule, preprint (2007) (New!!!)[PDF]

Download Slides

1.      Food Chain Chaos

2.      What do your DNA and DSL have in common? 

3.      Neuron Circuits and Communication

4.      Trapper Drove Lynx to Eat Hare

5.      Neural Basis of the Golden Ratio