» Articles » PMID: 3207954

Parameter-dependent Transitions and the Optimal Control of Dynamical Diseases

Overview
Journal Bull Math Biol
Publisher Springer
Specialties Biology
Public Health
Date 1988 Jan 1
PMID 3207954
Citations 3
Authors
Affiliations
Soon will be listed here.
Citing Articles

ABSENCE SEIZURES AS RESETTING MECHANISMS OF BRAIN DYNAMICS.

Nair S, Jukkola P, Quigley M, Wilberger A, Shiau D, Sackellares J Cybern Syst Anal. 2009; 44(5):664-672.

PMID: 19763248 PMC: 2745162. DOI: 10.1007/s10559-008-9051-7.


An investigation of EEG dynamics in an animal model of temporal lobe epilepsy using the maximum Lyapunov exponent.

Nair S, Shiau D, Principe J, Iasemidis L, Pardalos P, Norman W Exp Neurol. 2008; 216(1):115-21.

PMID: 19100262 PMC: 2643305. DOI: 10.1016/j.expneurol.2008.11.009.


Seizure prediction.

Sackellares J Epilepsy Curr. 2008; 8(3):55-9.

PMID: 18488065 PMC: 2384160. DOI: 10.1111/j.1535-7511.2008.00236.x.

References
1.
Swan G, Vincent T . Optimal control analysis in the chemotherapy of IgG multiple myeloma. Bull Math Biol. 1977; 39(3):317-37. DOI: 10.1007/BF02462912. View

2.
Goldberger A, Findley L, Blackburn M, Mandell A . Nonlinear dynamics in heart failure: implications of long-wavelength cardiopulmonary oscillations. Am Heart J. 1984; 107(3):612-5. DOI: 10.1016/0002-8703(84)90120-0. View

3.
WALTER C . The occurrence and the significance of limit cycle behavior in controlled biochemical systems. J Theor Biol. 1970; 27(2):259-72. DOI: 10.1016/0022-5193(70)90141-4. View

4.
Goldbeter A, Segel L . Control of developmental transitions in the cyclic AMP signalling system of Dictyostelium discoideum. Differentiation. 1980; 17(3):127-35. DOI: 10.1111/j.1432-0436.1980.tb01090.x. View

5.
Guevara M, Glass L . Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: a theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias. J Math Biol. 1982; 14(1):1-23. DOI: 10.1007/BF02154750. View