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Franke, John E.

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 Author ID: franke.john-e Published as: Franke, John E.; Franke, J. E.; Franke, John; Franke, J.
 Documents Indexed: 50 Publications since 1973
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Co-Authors

 3 single-authored 26 Yakubu, Abdul-Aziz 7 Selgrade, James F. 6 Block, Louis Stuart 4 Chan, David M. 1 Bidwell, John 1 Churchill, Richard C. 1 Faulkner, Gary D. 1 Janos, Ludvik 1 Ladas, Gerasimos E. 1 Morena, Matthew A.
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Serials

 8 Proceedings of the American Mathematical Society 7 Journal of Difference Equations and Applications 5 Journal of Mathematical Analysis and Applications 4 Journal of Mathematical Biology 4 Nonlinear Analysis. Theory, Methods & Applications 2 The Canadian Applied Mathematics Quarterly 2 Journal of Biological Dynamics 1 Computers & Mathematics with Applications 1 Mathematical Biosciences 1 Bulletin of Mathematical Biology 1 Inventiones Mathematicae 1 Journal of Differential Equations 1 Transactions of the American Mathematical Society 1 Ergodic Theory and Dynamical Systems 1 Mathematical and Computer Modelling 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 International Journal of Applied Mathematics and Computer Science 1 Nonlinear Analysis. Real World Applications 1 Mathematical Biosciences and Engineering 1 Research in Number Theory
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Fields

 33 Biology and other natural sciences (92-XX) 32 Dynamical systems and ergodic theory (37-XX) 23 Difference and functional equations (39-XX) 6 General topology (54-XX) 4 Ordinary differential equations (34-XX) 3 Measure and integration (28-XX) 2 Number theory (11-XX) 2 Numerical analysis (65-XX) 1 Real functions (26-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Systems theory; control (93-XX)

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