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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.

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

3. Good Health and Well-being
(Web of Science)

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.

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.

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.

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

3. Good Health and Well-being
(Web of Science)

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.

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.

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.

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

3. Good Health and Well-being
(Web of Science)

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.

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

3. Good Health and Well-being
(Web of Science)

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.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

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.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

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.

author keywords: attenuance; periodic carrying capacity; periodic survival rate; resonance

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

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.

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.

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

3. Good Health and Well-being
(Web of Science)

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.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

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.

author keywords: extinction; Lyapunov function; omega-limit set; weakly dominate; competition

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

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.

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

3. Good Health and Well-being
(Web of Science)

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.

author keywords: global attractivity; two-cycle; population model

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

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.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

10. Reduced Inequalities
(OpenAlex)

Source: Web Of Science

Added: August 6, 2018

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