John E Franke

Works (18)

2012 journal article

Predicting attenuant and resonant 2-cycles in periodically forced discrete-time two-species population models

JOURNAL OF BIOLOGICAL DYNAMICS, 6(2), 782–812.

By: M. Morena* & J. Franke

author keywords: attenuance; competition; periodic forcing; resonance; signature function
Source: Web Of Science
Added: August 6, 2018

2011 journal article

PERIODICALLY FORCED DISCRETE-TIME SIS EPIDEMIC MODEL WITH DISEASE INDUCED MORTALITY

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 8(2), 385–408.

By: J. Franke & A. Yakubu n

author keywords: Epidemics; infectives; periodic environments; susceptibles
Source: Web Of Science
Added: August 6, 2018

2008 journal article

Disease-induced mortality in density-dependent discrete-time S-I-S epidemic models

JOURNAL OF MATHEMATICAL BIOLOGY, 57(6), 755–790.

By: J. Franke & A. Yakubu

author keywords: basin of attraction; disease-induced mortality; multiple attractors
Source: Web Of Science
Added: August 6, 2018

2007 article

Using a signature function to determine resonant and attenuant 2-cycles in the Smith-Slatkin population model

Franke, J. E., & Yakubu, A.-A. (2007, April). JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, Vol. 13, pp. 289–308.

By: J. Franke & A. Yakubu*

author keywords: attenuant; periodic forcing; resonant; signature function; Smith-Slatkin model
Source: Web Of Science
Added: August 6, 2018

2006 journal article

Asymptotic behavior of Markov semigroups on preduals of von Neumann algebras

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 314(2), 749–763.

By: E. Ernel'yanov & M. Wolff*

author keywords: von neumann algebra; predual; Markov operator; mean ergodicity; statistical stability; domination
Source: Web Of Science
Added: August 6, 2018

2006 journal article

Discrete-time sis epidemic model in a seasonal environment

SIAM JOURNAL ON APPLIED MATHEMATICS, 66(5), 1563–1587.

By: J. Franke & A. Yakubu

author keywords: epidemics; infectives; periodic environments; susceptibles
Source: Web Of Science
Added: August 6, 2018

2006 journal article

Globally attracting attenuant versus resonant cycles in periodic compensatory Leslie models

MATHEMATICAL BIOSCIENCES, 204(1), 1–20.

By: J. Franke & A. Yakubu*

Source: Web Of Science
Added: August 6, 2018

2006 journal article

Signature function for predicting resonant and attenuant population 2-cycles

BULLETIN OF MATHEMATICAL BIOLOGY, 68(8), 2069–2104.

By: J. Franke & A. Yakubu

author keywords: attenuance; periodic carrying capacity; periodic demographic characteristic; signature function; resonance
Source: Web Of Science
Added: August 6, 2018

2005 journal article

Multiple attractors via CUSP bifurcation in periodically varying environments

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 11(4-5), 365–377.

By: J. Franke & A. Yakubu*

author keywords: periodic dynamical systems; semi-conjugacy; tangent bifurcation; multiple attractors
Source: Web Of Science
Added: August 6, 2018

2005 journal article

Periodic dynamical systems in unidirectional metapopulation models

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 11(7), 687–700.

By: J. Franke & A. Yakubu*

author keywords: metapopulation; multiple attractors; nonautonomous models; periodic dynamical systems; unidirectional dispersal
Source: Web Of Science
Added: August 6, 2018

2005 journal article

Population models with periodic recruitment functions and survival rates

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 11(14), 1169–1184.

By: J. Franke & A. Yakubu*

author keywords: attenuance; periodic carrying capacity; periodic survival rate; resonance
Source: Web Of Science
Added: August 6, 2018

2004 journal article

Probabilities of extinction, weak extinction permanence, and mutual exclusion in discrete, competitive, Lotka-Volterra systems

Computers & Mathematics With Applications, 47(03-Feb), 365–379.

By: D. Chan & J. Franke

Source: NC State University Libraries
Added: August 6, 2018

2004 journal article

Probabilities of extinction, weak extinction, permanence, and mutual exclusion in discrete, competitive, Lotka-Volterra systems that involve invading species

MATHEMATICAL AND COMPUTER MODELLING, 40(7-8), 809–821.

By: D. Chan & J. Franke

author keywords: extinction; permanence; mutual exclusion; competition; Lotka-Volterra; weak extinction; invader; strongly permanent
Source: Web Of Science
Added: August 6, 2018

2003 journal article

Attractors for discrete periodic dynamical systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 286(1), 64–79.

By: J. Franke & J. Selgrade

Source: Web Of Science
Added: August 6, 2018

2001 journal article

Multiple extinctions in a discrete competitive system

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2(1), 75–91.

By: D. Chan & J. Franke

author keywords: extinction; Lyapunov function; omega-limit set; weakly dominate; competition
Source: Web Of Science
Added: August 6, 2018

1999 journal article

Exclusionary population dynamics in size-structured, discrete competitive systems

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 5(3), 235–249.

By: J. Francke & A. Yakubu

author keywords: extinction; Lyapunov function; chaotic attractor
Source: Web Of Science
Added: August 6, 2018

1999 journal article

Global attractivity and convergence to a two-cycle in a difference equation

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 5(2), 203–209.

By: J. Franke, J. Hoag & G. Ladas

author keywords: global attractivity; two-cycle; population model
Source: Web Of Science
Added: August 6, 2018

1997 article

Principles of competitive exclusion for discrete populations with reproducing juveniles and adults

Franke, J. E., & Yakubu, A. A. (1997, December). NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, Vol. 30, pp. 1197–1205.

By: J. Franke & A. Yakubu*

Source: Web Of Science
Added: August 6, 2018