A Note on Attenuant Cycles of Population Models with Periodic Carrying Capacity

Kon, Ryusuke

doi:10.1080/10236190410001703949

Cited by 39 publications

(29 citation statements)

References 2 publications

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“…In [9] the authors conjectured that cycles in a population governed by a scalar Beverton-Holt nonlinear difference equation with periodic carrying capacity are attenuant for all periods. This conjecture was confirmed in many papers including [12,13,14,24,25,26].…”

Section: Introductionsupporting

confidence: 52%

The global dynamics of a discrete juvenile–adult model with continuous and seasonal reproduction

Ackleh

Chiquet

2009

Journal of Biological Dynamics

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A general discrete juvenile-adult population model with time-dependent birth rate and nonlinear survivorship rates is studied. When breeding is continuous, it is shown that the model has a unique globally asymptotically stable positive equilibrium provided the net reproductive number is larger than one. If it is smaller than one, then the extinction equilibrium is globally asymptotically stable. When breeding is seasonal, it is shown that there exists a unique globally asymptotically stable periodic solution provided the net reproductive number is larger than one. When this value is less than one, the population goes to extinction. Conditions on the birth rate where the population with seasonal breeding survives while the population with continuous breeding becomes extinct are provided.

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Section: Introductionsupporting

confidence: 52%

The global dynamics of a discrete juvenile–adult model with continuous and seasonal reproduction

Ackleh

Chiquet

2009

Journal of Biological Dynamics

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“…Using these models, we study the effects of almost periodic forcing of the carrying capacity, the demographic characteristic and survival rates of species on the long-term behavior of discretely reproducing populations. Others have studied the effects of periodic forcing of the carrying capacity, the demographic characteristic and survival rates of species on population dynamics [8,9,10], [12,13,14,15,16], [20,21,22,23,24], [28,29,30,31], and [34,35,36,37]. Typically, such periodically forced models support attracting cycles that are either enhance via resonance or diminished via attenuance.…”

Section: Resultsmentioning

confidence: 99%

“…Jillson performed such an experiment with laboratory cultures of Tribolium [34]. Others have used mathematical models to study the effects of periodic forcing on population dynamics [8,9,10], [12,13,14,15,16,17], [20,21,22,23,24], [29,30], and [35,36,37,38].…”

Section: Introductionmentioning

confidence: 99%

“…Despite the fact that all natural populations suffer temporal environmental fluctuations on some scale, experimental and theoretical studies of population responses to external fluctuations remain relatively rare [8,9,10], [12,13,14,15,16,17], [20,21,22,23,24], [28,29,30], [32], and [35,36,36,38,39,40,41]. To study the effects of fluctuating environments on population dynamics, one can deliberately fluctuate environmental parameters in controlled laboratory experiments.…”

Section: Introductionmentioning

confidence: 99%

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Population models in almost periodic environments

Diagana

Elaydi

Yakubu

2007

Journal of Difference Equations and Applications

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Abstract. We establish the basic theory of almost periodic sequences on Z + . Dichotomy techniques are then utilized to find sufficient conditions for the existence of a globally attracting almost periodic solution of a semilinear system of difference equations. These existence results are, subsequently, applied to discretely reproducing populations with and without overlapping generations. Furthermore, we access evidence for attenuance and resonance in almost periodically forced population models.

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“…Independently, Ryusuke Kon in [19] and [20] established (C2) for an even wider class of maps including Ricker type maps with restrictions. Also Kocic [18] has given a solution to (C2).…”

Section: Introductionmentioning

confidence: 99%

The Stochastic Beverton-Holt Equation and the M. Neubert Conjecture

Haskell

Sacker

2005

J Dyn Diff Equat

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In the Beverton Holt difference equation of population biology with intrinsic growth parameter above its critical value, any initial non-zero population will approach an asymptotically stable fixed point, the carrying capacity of the environment. When this carrying capacity is allowed to vary periodically it is known that there is a globally asymptotically stable periodic solution and the average of the state variable along this solution is strictly less than the average of the carrying capacities, i.e. the varying environment has a deleterious effect on the state average. In this work we consider the case of a randomly varying environment and show that there is a unique invariant density to which all other density distributions on the state variable converge. Further, for every initial non-zero state variable and almost all random sequences of carrying capacities, the averages of the state variable along an orbit and the carrying capacities exist and the former is strictly less than the latter.

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A Note on Attenuant Cycles of Population Models with Periodic Carrying Capacity

Cited by 39 publications

References 2 publications

The global dynamics of a discrete juvenile–adult model with continuous and seasonal reproduction

The global dynamics of a discrete juvenile–adult model with continuous and seasonal reproduction

Population models in almost periodic environments

The Stochastic Beverton-Holt Equation and the M. Neubert Conjecture

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