John E. Franke

Works (18)

Updated: April 4th, 2024 17:14

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
MeSH headings : Conservation of Natural Resources; Models, Biological; Periodicity; Population Dynamics; Species Specificity; Time Factors
TL;DR: This work derives signature functions for predicting the responses of two competing populations to 2-periodic oscillations in six model parameters that include the Logistic, Ricker, Beverton–Holt, and Hassell models. (via Semantic Scholar)
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
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 n & A. Yakubu n

author keywords: Epidemics; infectives; periodic environments; susceptibles
TL;DR: The Beverton-Holt recruitment function is used to show that the infective population exhibits period-doubling bifurcations route to chaos where the disease-free susceptible population lives on a 2-cycle (non-chaotic) attractor. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
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 n & A. Yakubu*

author keywords: basin of attraction; disease-induced mortality; multiple attractors
MeSH headings : Biometry; Disease; Disease Outbreaks / statistics & numerical data; Humans; Mathematics; Models, Statistical; Mortality
TL;DR: This work uses a Ricker recruitment function in an SIS model and obtained a three component discrete Hopf (Neimark–Sacker) cycle attractor coexisting with a fixed point attractor, showing that in contrast to corresponding models without disease-induced mortality, the disease-free state dynamics do not drive the disease dynamics. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
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 n & A. Yakubu*

author keywords: attenuant; periodic forcing; resonant; signature function; Smith-Slatkin model
TL;DR: It is proved that small 2-periodic fluctuations of the three parameters generate 2-cyclic oscillations of the population and a signature function is developed for predicting the responses of populations to 2- periodic fluctuations. (via Semantic Scholar)
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
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
TL;DR: It is shown that in periodic environments, it is possible for the infective population to be on a chaotic attractor while the demographic dynamics is nonchaotic. (via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being (Web of Science; OpenAlex)
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 n & A. Yakubu*

MeSH headings : Animals; Biological Clocks; Ecosystem; Models, Biological; Population Dynamics; Tribolium / growth & development
TL;DR: The results show that the response of age-structured populations to environmental fluctuations is a complex function of the compensatory mechanisms at different life-history stages, the fertile age classes and the period of the environment. (via Semantic Scholar)
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
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 n & A. Yakubu*

author keywords: attenuance; periodic carrying capacity; periodic demographic characteristic; signature function; resonance
MeSH headings : Animals; Ecosystem; Models, Biological; Population Dynamics
TL;DR: A signature function for predicting the response of discretely reproducing populations to 2-periodic fluctuations of both a characteristic of the environment (carrying capacity), and a characteristics of the population (inherent growth rate) is developed. (via Semantic Scholar)
UN Sustainable Development Goal Categories
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 n & A. Yakubu*

author keywords: periodic dynamical systems; semi-conjugacy; tangent bifurcation; multiple attractors
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
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 n & 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 n & 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 n

author keywords: extinction; permanence; mutual exclusion; competition; Lotka-Volterra; weak extinction; invader; strongly permanent
TL;DR: The probabilities of various biological asymptotic dynamics are computed for a stable system that is invaded by another competing species and it is found that multiple extinctions that include the invading species and one of the original species are impossible. (via Semantic Scholar)
UN Sustainable Development Goal Categories
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 n & J. Selgrade n

TL;DR: A structure theorem is established which says that the attractor of a time-periodic dynamical system is the union of attractors of appropriate autonomous maps, and properties that the nonautonomous attractor inherits from the autonomous attractor are discussed. (via Semantic Scholar)
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 n & J. Franke n

author keywords: extinction; Lyapunov function; omega-limit set; weakly dominate; competition
UN Sustainable Development Goal Categories
13. Climate Action (OpenAlex)
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
TL;DR: A discrete multi-species size-structured competition model is considered and by using decreasing growth functions, the self-regulation of species is achieved by using decrease growth functions to achieve coexistence in a chaotic supr transient. (via Semantic Scholar)
UN Sustainable Development Goal Categories
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 n, J. Hoag* & G. Ladas*

author keywords: global attractivity; two-cycle; population model
UN Sustainable Development Goal Categories
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 n & A. Yakubu*

TL;DR: It is shown that if juveniles are allowed to reproduce, then a weakly dominant species could be driven to extinction, provided all the growth functions are exponentials. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

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