DOI: 10.1016/0378-4371(78)90213-3. Deterministic and stochastic theory of sustained oscillations in autocatalytic reaction systems

Deterministic and stochastic theory of sustained oscillations in autocatalytic reaction systems

10.1016/0378-4371(78)90213-3

Crossref journal-article

Elsevier BV

Physica A: Statistical Mechanics and its Applications (78)

Bibliography

Feistel, R., & Ebeling, W. (1978). Deterministic and stochastic theory of sustained oscillations in autocatalytic reaction systems. Physica A: Statistical Mechanics and Its Applications, 93(1â2), 114â137.

Authors 2

R. Feistel (first)
W. Ebeling (additional)

References 38 Referenced 26

{'key': '10.1016/0378-4371(78)90213-3_BIB1', 'author': 'Andronov', 'year': '1969', 'journal-title': 'Theorie der Schwingungen'} / Theorie der Schwingungen by Andronov (1969)
{'key': '10.1016/0378-4371(78)90213-3_BIB2', 'volume': 'Bd. II', 'year': '1966'} (1966)
{'key': '10.1016/0378-4371(78)90213-3_BIB3', 'author': 'Glansdorff', 'year': '1971', 'journal-title': 'Thermodynamic Theory of Structure, Stability and Fluctuations'} / Thermodynamic Theory of Structure, Stability and Fluctuations by Glansdorff (1971)
{'key': '10.1016/0378-4371(78)90213-3_BIB4', 'series-title': 'Strukturbildung bei irreversiblen Prozessen', 'author': 'Ebeling', 'year': '1976'} / Strukturbildung bei irreversiblen Prozessen by Ebeling (1976)
{'key': '10.1016/0378-4371(78)90213-3_BIB5', 'first-page': '306', 'volume': '9', 'author': 'Zhabotinsky', 'year': '1964', 'journal-title': 'Biofizika'} / Biofizika by Zhabotinsky (1964)
10.1021/ie50689a006 / Ind. Eng. Chem. by Higgins (1967)
10.1021/cr60284a003 / Chem. Rev. by Nicolis (1973)
10.1002/anie.197800013 / Angew. Chem. Int. Ed. Engl. by Franck (1978)
10.1063/1.1841255 / J. Chem. Phys. by Prigogine (1967)
10.1063/1.1668896 / J. Chem. Phys. by Prigogine (1968)
10.1007/BF01395916 / Z. Phys. by Schlögl (1971)
10.1007/BF01395694 / Z. Phys. by Schlögl (1971)
10.1007/BF01379769 / Z. Phys. by Schlögl (1972)
10.1063/1.1681974 / J. Chem. Phys. by Nitzan (1974)
{'key': '10.1016/0378-4371(78)90213-3_BIB8_5', 'series-title': 'Introduction to Synergetics', 'author': 'Haken', 'year': '1977'} / Introduction to Synergetics by Haken (1977)
10.1515/zpch-1976-25779 / Z. Phys. Chem. (Leipzig) by Ebeling (1976)
{'key': '10.1016/0378-4371(78)90213-3_BIB9_2', 'first-page': '81', 'volume': '34', 'year': '1977', 'journal-title': 'Ann. Phys. (Leipzig)'} / Ann. Phys. (Leipzig) (1977)
{'key': '10.1016/0378-4371(78)90213-3_BIB10', 'series-title': 'Proc. ICNO', 'author': 'Ebeling', 'year': '1975'} / Proc. ICNO by Ebeling (1975)
10.1111/j.1432-1033.1968.tb00175.x / Europ. J. Biochem. by Sel'kov (1968)
{'key': '10.1016/0378-4371(78)90213-3_BIB12', 'first-page': '862', 'volume': '17', 'author': 'Samoylenko', 'year': '1972', 'journal-title': 'Biofizika (Moscow)'} / Biofizika (Moscow) by Samoylenko (1972)
10.1143/PTP.51.1731 / Progr. Theor. Phys. by Tomita (1974)
{'key': '10.1016/0378-4371(78)90213-3_BIB13_2', 'first-page': '484', 'volume': '52', 'author': 'Tomita', 'year': '1974', 'journal-title': 'Progr. Theor. Phys.'} / Progr. Theor. Phys. by Tomita (1974)
10.1016/0375-9601(76)90664-2 / Phys. Lett. by Ibanez (1976)
W. Ebeling, R. Feistel and J. Schmelzer, Wiss. Z.W. Pieck Univ., Rostock, MNR, in press.
J.L. Ibanez and M.G. Velarde, Studies Appl. Math., in press.
{'key': '10.1016/0378-4371(78)90213-3_BIB16', 'author': 'Landau', 'year': '1957', 'journal-title': 'Statistical Physics'} / Statistical Physics by Landau (1957)
{'key': '10.1016/0378-4371(78)90213-3_BIB17', 'author': 'Nicolis', 'year': '1977', 'journal-title': 'Selforganization in Nonequilibrium Systems'} / Selforganization in Nonequilibrium Systems by Nicolis (1977)
10.1007/BF01020400 / J. Stat. Phys. by McNeil (1974)
10.1007/BF01030197 / J. Stat. Phys. by Gardiner (1976)
10.1515/jnet.1977.2.1.1 / J. Non-Equilib. Thermodyn. by Czajkowski (1977)
10.1007/BF01395700 / Z. Phys. by Drosdziok (1973)
{'key': '10.1016/0378-4371(78)90213-3_BIB21', 'volume': 'Bd.II', 'author': 'Gantmacher', 'year': '1971', 'journal-title': 'Matrizenrechnung'} / Matrizenrechnung by Gantmacher (1971)
{'key': '10.1016/0378-4371(78)90213-3_BIB22', 'article-title': 'Stochastic Processes in Physics', 'author': 'van Kampen', 'year': '1970', 'journal-title': 'Lecture notes'} / Lecture notes / Stochastic Processes in Physics by van Kampen (1970)
{'key': '10.1016/0378-4371(78)90213-3_BIB23', 'author': 'Uhlmann', 'year': '1977', 'journal-title': 'Stochastische Theorie Nichtlinearer Irreversibler Prozesse'} / Stochastische Theorie Nichtlinearer Irreversibler Prozesse by Uhlmann (1977)
{'key': '10.1016/0378-4371(78)90213-3_BIB24', 'first-page': '411', 'volume': 'B25', 'author': 'Schlögl', 'year': '1976', 'journal-title': 'Z. Phys.'} / Z. Phys. by Schlögl (1976)
10.1007/BF01676796 / Z. Phys. by Janssen (1974)
G. Czajkowski, Acta Phys. Polonica, in press.
{'key': '10.1016/0378-4371(78)90213-3_BIB27', 'volume': 'vols. I,II', 'author': 'Stratonovich', 'year': '1967', 'journal-title': 'Topics in the Theory of Random Noise'} / Topics in the Theory of Random Noise by Stratonovich (1967)

Dates

Type	When
Created	22 years, 10 months ago (Oct. 17, 2002, 12:26 p.m.)
Deposited	2 years, 4 months ago (April 24, 2023, 8:01 p.m.)
Indexed	1 month ago (Aug. 2, 2025, 12:09 a.m.)
Issued	47 years, 1 month ago (Aug. 1, 1978)
Published	47 years, 1 month ago (Aug. 1, 1978)
Published Print	47 years, 1 month ago (Aug. 1, 1978)

Funders 0

None

BibTeX

@article{Feistel_1978, title={Deterministic and stochastic theory of sustained oscillations in autocatalytic reaction systems}, volume={93}, ISSN={0378-4371}, url={http://dx.doi.org/10.1016/0378-4371(78)90213-3}, DOI={10.1016/0378-4371(78)90213-3}, number={1–2}, journal={Physica A: Statistical Mechanics and its Applications}, publisher={Elsevier BV}, author={Feistel, R. and Ebeling, W.}, year={1978}, month=aug, pages={114–137} }

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