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Franke, John E.

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Author ID: franke.john-e Recent zbMATH articles by "Franke, John E."
Published as: Franke, John E.; Franke, J. E.; Franke, John; Franke, J.
Documents Indexed: 50 Publications since 1973

Publications by Year

Citations contained in zbMATH Open

44 Publications have been cited 487 times in 292 Documents Cited by Year
Mutual exclusion versus coexistence for discrete competitive systems. Zbl 0735.92023
Franke, John E.; Yakubu, Abdul-Aziz
62
1991
Geometry of exclusion principles in discrete systems. Zbl 0778.93012
Franke, John E.; Yakubu, Abdul-Aziz
41
1992
Attractors for discrete periodic dynamical systems. Zbl 1035.37020
Franke, John E.; Selgrade, James F.
33
2003
Hyperbolicity and chain recurrence. Zbl 0329.58012
Franke, John E.; Selgrade, James F.
30
1977
Discrete-time SIS epidemic model in a seasonal environment. Zbl 1108.37303
Franke, John E.; Yakubu, Abdul-Aziz
25
2006
Global attractors in competitive systems. Zbl 0724.92024
Franke, John E.; Yakubu, Abdul-Aziz
18
1991
Disease-induced mortality in density-dependent discrete-time S-I-S epidemic models. Zbl 1161.92046
Franke, John E.; Yakubu, Abdul-Aziz
17
2008
Extinction and persistence of species in discrete competitive systems with a safe refuge. Zbl 0864.92016
Franke, John E.; Yakubu, Abdul-Aziz
15
1996
Global attractivity and convergence to a two-cycle in a difference equation. Zbl 0927.39005
Franke, J. E.; Hoag, J. T.; Ladas, G.
15
1999
Periodic dynamical systems in unidirectional metapopulation models. Zbl 1070.92049
Franke, John E.; Yakubu, Abdul-Aziz
15
2005
Existence of periodic points for maps of S\(^1\). Zbl 0272.58005
Block, Louis; Franke, John
15
1973
The chain recurrent set, attractors, and explosions. Zbl 0572.54037
Block, Louis; Franke, John E.
15
1985
Abstract \(\omega\)-limit sets, chain recurrent sets, and basic sets for flows. Zbl 0316.58014
Franke, John E.; Selgrade, James F.
14
1977
Pioneer exclusion in a one-hump discrete pioneer-climax competitive system. Zbl 0828.92029
Franke, John E.; Yakubu, Abdul-Aziz
13
1994
Multiple attractors via CUSP bifurcation in periodically varying environments. Zbl 1068.92038
Franke, John E.; Yakubu, Abdul-Aziz
12
2005
Population models with periodic recruitment functions and survival rates. Zbl 1079.92063
Franke, John E.; Yakubu, Abdul-Aziz
12
2005
Attenuant cycles in periodically forced discrete-time age-structured population models. Zbl 1083.92037
Franke, John E.; Yakubu, Abdul-Aziz
10
2006
Signature function for predicting resonant and attenuant population 2-cycles. Zbl 1296.92203
Franke, John E.; Yakubu, Abdul-Aziz
10
2006
Exclusion principles for density-dependent discrete pioneer-climax models. Zbl 0840.92027
Franke, John E.; Yakubu, Abdul-Aziz
10
1994
Multiple extinctions in a discrete competitive system. Zbl 1014.92038
Chan, David M.; Franke, John E.
10
2001
The chain recurrent set for maps of the interval. Zbl 0513.54025
Block, Louis; Franke, John E.
10
1983
Globally attracting attenuant versus resonant cycles in periodic compensatory Leslie models. Zbl 1104.92060
Franke, John E.; Yakubu, Abdul-Aziz
9
2006
A geometric criterion for hyperbolicity of flows. Zbl 0316.58015
Churchill, R. C.; Franke, John; Selgrade, James
7
1977
Species extinction using geometry of level surfaces. Zbl 0788.34043
Franke, John E.; Yakubu, Abdul-Aziz
7
1993
Periodically forced discrete-time SIS epidemic model with disease induced mortality. Zbl 1259.37058
Franke, John E.; Yakubu, Abdul-Aziz
6
2011
Extinction of species in age-structured, discrete noncooperative systems. Zbl 0840.92026
Franke, John E.; Yakubu, Abdul-Aziz
5
1996
Principles of competitive exclusion for discrete populations with reproducing juveniles and adults. Zbl 0894.92031
Franke, John E.; Yakubu, Abdul-Aziz
5
1997
A classification of the structurally stable contracting endomorphisms of S\(^1\). Zbl 0263.58010
Block, Louis; Franke, John
5
1973
Abstract \(\omega\)-limit sets, chain recurrent sets, and basic sets for flows. Zbl 0334.58010
Franke, John E.; Selgrade, James F.
4
1977
Hyperbolicity and cycles. Zbl 0396.58023
Franke, J. E.; Selgrade, J. F.
4
1978
Probabilities of extinction, weak extinction permanence, and mutual exclusion in discrete, competitive, Lotka-Volterra systems. Zbl 1043.92036
Chan, D. M.; Franke, J. E.
4
2004
Bounded implies eventually periodic for the positive case of reciprocal-max difference equation with periodic parameters. Zbl 1143.39003
Bidwell, John; Franke, John E.
4
2008
Using a signature function to determine resonant and attenuant 2-cycles in the Smith-Slatkin population model. Zbl 1110.92036
Franke, John E.; Yakubu, Abdul-Aziz
3
2007
Exclusionary population dynamics in size-structured, discrete competitive systems. Zbl 0934.37042
Franke, John E.; Yakubu, Abdul-Aziz
3
1999
The chain recurrent set for maps of the circle. Zbl 0524.54030
Block, Louis; Franke, John E.
3
1984
Extinction, weak extinction and persistence in a discrete, competitive Lotka-Volterra model. Zbl 0951.92028
Chan, David M.; Franke, John E.
3
2000
Diffusion between patches in multi-species discrete competitive systems. Zbl 0888.92036
Franke, John E.; Yakubu, Abdul-Aziz
2
1997
A computer method for verification of asymptotically stable periodic orbits. Zbl 0413.34053
Franke, John E.; Selgrade, James F.
2
1979
Probabilities of extinction, weak extinction, permanence, and mutual exclusion in discrete, competitive, Lotka-Volterra systems that involve invading species. Zbl 1066.92049
Chan, D. M.; Franke, J. E.
2
2004
Isolated chain recurrent points for one-dimensional maps. Zbl 0567.54025
Block, Louis; Franke, John E.
2
1985
Rational functions and modular forms. Zbl 1452.11047
Franke, J.
2
2020
Extinction in systems of bobwhite quail populations. Zbl 0838.92028
Franke, John E.; Yakubu, Abdul-Aziz
1
1995
Global asymptotic behavior and dispersion in age-structured, discrete competitive systems. Zbl 0912.92031
Franke, John E.; Yakubu, Abdul-Aziz
1
1997
SIS epidemic attractors in periodic environments. Zbl 1284.92102
Franke, John E.; Yakubu, Abdul-Aziz
1
2007
Rational functions and modular forms. Zbl 1452.11047
Franke, J.
2
2020
Periodically forced discrete-time SIS epidemic model with disease induced mortality. Zbl 1259.37058
Franke, John E.; Yakubu, Abdul-Aziz
6
2011
Disease-induced mortality in density-dependent discrete-time S-I-S epidemic models. Zbl 1161.92046
Franke, John E.; Yakubu, Abdul-Aziz
17
2008
Bounded implies eventually periodic for the positive case of reciprocal-max difference equation with periodic parameters. Zbl 1143.39003
Bidwell, John; Franke, John E.
4
2008
Using a signature function to determine resonant and attenuant 2-cycles in the Smith-Slatkin population model. Zbl 1110.92036
Franke, John E.; Yakubu, Abdul-Aziz
3
2007
SIS epidemic attractors in periodic environments. Zbl 1284.92102
Franke, John E.; Yakubu, Abdul-Aziz
1
2007
Discrete-time SIS epidemic model in a seasonal environment. Zbl 1108.37303
Franke, John E.; Yakubu, Abdul-Aziz
25
2006
Attenuant cycles in periodically forced discrete-time age-structured population models. Zbl 1083.92037
Franke, John E.; Yakubu, Abdul-Aziz
10
2006
Signature function for predicting resonant and attenuant population 2-cycles. Zbl 1296.92203
Franke, John E.; Yakubu, Abdul-Aziz
10
2006
Globally attracting attenuant versus resonant cycles in periodic compensatory Leslie models. Zbl 1104.92060
Franke, John E.; Yakubu, Abdul-Aziz
9
2006
Periodic dynamical systems in unidirectional metapopulation models. Zbl 1070.92049
Franke, John E.; Yakubu, Abdul-Aziz
15
2005
Multiple attractors via CUSP bifurcation in periodically varying environments. Zbl 1068.92038
Franke, John E.; Yakubu, Abdul-Aziz
12
2005
Population models with periodic recruitment functions and survival rates. Zbl 1079.92063
Franke, John E.; Yakubu, Abdul-Aziz
12
2005
Probabilities of extinction, weak extinction permanence, and mutual exclusion in discrete, competitive, Lotka-Volterra systems. Zbl 1043.92036
Chan, D. M.; Franke, J. E.
4
2004
Probabilities of extinction, weak extinction, permanence, and mutual exclusion in discrete, competitive, Lotka-Volterra systems that involve invading species. Zbl 1066.92049
Chan, D. M.; Franke, J. E.
2
2004
Attractors for discrete periodic dynamical systems. Zbl 1035.37020
Franke, John E.; Selgrade, James F.
33
2003
Multiple extinctions in a discrete competitive system. Zbl 1014.92038
Chan, David M.; Franke, John E.
10
2001
Extinction, weak extinction and persistence in a discrete, competitive Lotka-Volterra model. Zbl 0951.92028
Chan, David M.; Franke, John E.
3
2000
Global attractivity and convergence to a two-cycle in a difference equation. Zbl 0927.39005
Franke, J. E.; Hoag, J. T.; Ladas, G.
15
1999
Exclusionary population dynamics in size-structured, discrete competitive systems. Zbl 0934.37042
Franke, John E.; Yakubu, Abdul-Aziz
3
1999
Principles of competitive exclusion for discrete populations with reproducing juveniles and adults. Zbl 0894.92031
Franke, John E.; Yakubu, Abdul-Aziz
5
1997
Diffusion between patches in multi-species discrete competitive systems. Zbl 0888.92036
Franke, John E.; Yakubu, Abdul-Aziz
2
1997
Global asymptotic behavior and dispersion in age-structured, discrete competitive systems. Zbl 0912.92031
Franke, John E.; Yakubu, Abdul-Aziz
1
1997
Extinction and persistence of species in discrete competitive systems with a safe refuge. Zbl 0864.92016
Franke, John E.; Yakubu, Abdul-Aziz
15
1996
Extinction of species in age-structured, discrete noncooperative systems. Zbl 0840.92026
Franke, John E.; Yakubu, Abdul-Aziz
5
1996
Extinction in systems of bobwhite quail populations. Zbl 0838.92028
Franke, John E.; Yakubu, Abdul-Aziz
1
1995
Pioneer exclusion in a one-hump discrete pioneer-climax competitive system. Zbl 0828.92029
Franke, John E.; Yakubu, Abdul-Aziz
13
1994
Exclusion principles for density-dependent discrete pioneer-climax models. Zbl 0840.92027
Franke, John E.; Yakubu, Abdul-Aziz
10
1994
Species extinction using geometry of level surfaces. Zbl 0788.34043
Franke, John E.; Yakubu, Abdul-Aziz
7
1993
Geometry of exclusion principles in discrete systems. Zbl 0778.93012
Franke, John E.; Yakubu, Abdul-Aziz
41
1992
Mutual exclusion versus coexistence for discrete competitive systems. Zbl 0735.92023
Franke, John E.; Yakubu, Abdul-Aziz
62
1991
Global attractors in competitive systems. Zbl 0724.92024
Franke, John E.; Yakubu, Abdul-Aziz
18
1991
The chain recurrent set, attractors, and explosions. Zbl 0572.54037
Block, Louis; Franke, John E.
15
1985
Isolated chain recurrent points for one-dimensional maps. Zbl 0567.54025
Block, Louis; Franke, John E.
2
1985
The chain recurrent set for maps of the circle. Zbl 0524.54030
Block, Louis; Franke, John E.
3
1984
The chain recurrent set for maps of the interval. Zbl 0513.54025
Block, Louis; Franke, John E.
10
1983
A computer method for verification of asymptotically stable periodic orbits. Zbl 0413.34053
Franke, John E.; Selgrade, James F.
2
1979
Hyperbolicity and cycles. Zbl 0396.58023
Franke, J. E.; Selgrade, J. F.
4
1978
Hyperbolicity and chain recurrence. Zbl 0329.58012
Franke, John E.; Selgrade, James F.
30
1977
Abstract \(\omega\)-limit sets, chain recurrent sets, and basic sets for flows. Zbl 0316.58014
Franke, John E.; Selgrade, James F.
14
1977
A geometric criterion for hyperbolicity of flows. Zbl 0316.58015
Churchill, R. C.; Franke, John; Selgrade, James
7
1977
Abstract \(\omega\)-limit sets, chain recurrent sets, and basic sets for flows. Zbl 0334.58010
Franke, John E.; Selgrade, James F.
4
1977
Existence of periodic points for maps of S\(^1\). Zbl 0272.58005
Block, Louis; Franke, John
15
1973
A classification of the structurally stable contracting endomorphisms of S\(^1\). Zbl 0263.58010
Block, Louis; Franke, John
5
1973
all top 5

Cited by 347 Authors

39 Yakubu, Abdul-Aziz
28 Franke, John E.
20 Kulenović, Mustafa R. S.
15 Teng, Zhi-dong
11 Selgrade, James F.
10 Block, Louis Stuart
10 Elaydi, Saber Nasr
9 Dehghan Takht Fooladi, Mehdi
6 Alsharawi, Ziyad
6 Jaberi-Douraki, Majid
6 Sedaghat, Hassan
5 Chan, David M.
4 Cao, Hui
4 Hu, Zengyun
4 Jiang, Haijun
4 Pilav, Esmir
4 Sacker, Robert J.
4 Smith, Hal Leslie
4 Tresser, Charles
3 Ackleh, Azmy S.
3 Angelos, James R.
3 Arai, Zin
3 Bézandry, Paul Hubert
3 Cushing, Jim M.
3 Efremova, Lyudmila S.
3 Kang, Yun
3 Lazaryan, Nika
3 Mazrooei-Sebdani, Reza
3 Merino, Orlando
3 Nurkanovic, Mehmed
3 Palmer, Kenneth James
3 Razzaghi, Mohsen
3 Roberds, James H.
3 Thomas, Romeo F.
3 Wang, Wendi
3 Zhou, Yicang
3 Ziyadi, Najat
2 Allen, Linda J. S.
2 Athanassopoulos, Konstantin
2 Berenhaut, Kenneth S.
2 Blackmore, Denis L.
2 Brett, Ann
2 Camouzis, Elias
2 Chen, Liang
2 Chen, Xi
2 Chicone, Carmen C.
2 Clark, C. A.
2 Clark, Dean S.
2 Coomes, Brian A.
2 Diagana, Toka
2 Fogarty, Michael J.
2 Friedman, Avner
2 Gao, Shujing
2 Guy, Richard T.
2 Hadžiabdić, Vahidin
2 Haskell, Cymra
2 Hirsch, Morris W.
2 Hofbauer, Josef
2 Jang, Sophia R.-J.
2 Janowski, Ed J.
2 Kalabušić, Senada
2 Kato, Kazuhisa
2 Kent, Candace M.
2 Kifer, Yuri
2 Kocic, Vlajko Lj.
2 Ladas, Gerasimos E.
2 Lee, Manseob
2 Li, Weigu
2 Linero Bas, Antonio
2 Luís, Rafael
2 Mai, Jiehua
2 Mañosa, Víctor
2 Morimoto, Akihiko
2 Newhouse, Sheldon E.
2 Nie, Linfei
2 Nurkanović, Zehra
2 Shi, Yuming
2 Soler López, Gabriel
2 Swanson, Richard C.
2 van den Driessche, Pauline
2 Weng, Peixuan
2 Xu, Jiabo
2 Zeng, Fanping
2 Zhang, Gengrong
2 Zhang, Guang
2 Zhang, Qingling
2 Zou, Xingfu
1 Abdelaziz, Mahmoud A. M.
1 Abdelli, Hafedh
1 Abdullah, Farah Aini
1 Abu-Saris, Raghib M.
1 Al-Ghassani, Asma S.
1 Al-Hassan, Qassem M.
1 Al-Salman, Ahmad
1 Alidousti, Javad
1 Artalejo, Jesus R.
1 Ashwin, Peter
1 Askri, Ghassen
1 Ban, Hye Jin
1 Barrett, Christa L.
...and 247 more Authors
all top 5

Cited in 70 Serials

44 Journal of Difference Equations and Applications
17 Applied Mathematics and Computation
14 Advances in Difference Equations
12 Journal of Biological Dynamics
11 Journal of Mathematical Analysis and Applications
11 Journal of Differential Equations
10 Mathematical Biosciences
10 Proceedings of the American Mathematical Society
9 Computers & Mathematics with Applications
9 Chaos, Solitons and Fractals
8 Transactions of the American Mathematical Society
8 Discrete Dynamics in Nature and Society
8 Nonlinear Analysis. Theory, Methods & Applications
7 Journal of Mathematical Biology
7 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
7 Discrete and Continuous Dynamical Systems. Series B
6 Ergodic Theory and Dynamical Systems
5 Mathematical and Computer Modelling
4 Communications in Mathematical Physics
4 Topology and its Applications
4 Physica D
4 Journal of Mathematical Sciences (New York)
4 Discrete and Continuous Dynamical Systems
4 Nonlinear Analysis. Real World Applications
3 Bulletin of the Australian Mathematical Society
3 Inventiones Mathematicae
3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
3 Journal of Dynamics and Differential Equations
3 Nonlinear Dynamics
2 Mathematical Methods in the Applied Sciences
2 Rocky Mountain Journal of Mathematics
2 Bulletin of Mathematical Biology
2 Applied Mathematical Modelling
2 Chaos
2 Qualitative Theory of Dynamical Systems
2 Nonautonomous Dynamical Systems
1 Applicable Analysis
1 Israel Journal of Mathematics
1 Journal d’Analyse Mathématique
1 Journal of the Franklin Institute
1 Mathematical Notes
1 Periodica Mathematica Hungarica
1 Annales Polonici Mathematici
1 Boletim da Sociedade Brasileira de Matemática
1 Publications Mathématiques
1 Journal of Applied Probability
1 Journal of Computational and Applied Mathematics
1 Manuscripta Mathematica
1 Mathematische Zeitschrift
1 Monatshefte für Mathematik
1 Nagoya Mathematical Journal
1 Quaestiones Mathematicae
1 Theoretical Population Biology
1 Applied Mathematics Letters
1 Science in China. Series A
1 Japan Journal of Industrial and Applied Mathematics
1 Acta Mathematica Sinica. New Series
1 Tatra Mountains Mathematical Publications
1 Complexity
1 Differential Equations and Dynamical Systems
1 Abstract and Applied Analysis
1 Communications in Nonlinear Science and Numerical Simulation
1 Dynamical Systems
1 Advanced Nonlinear Studies
1 Communications on Pure and Applied Analysis
1 Journal of Applied Mathematics and Computing
1 Afrika Matematika
1 Journal of Theoretical Biology
1 Axioms
1 Journal of Mathematics

Citations by Year