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Full-Text Articles in Physical Sciences and Mathematics
Non-Autonomous Periodic Systems With Allee Effects, Rafael Luis, Saber Elaydi, Henrique Oliveira
Non-Autonomous Periodic Systems With Allee Effects, Rafael Luis, Saber Elaydi, Henrique Oliveira
Saber Elaydi
A new class of maps called unimodal Allee maps are introduced. Such maps arise in the study of population dynamics in which the population goes extinct if its size falls below a threshold value. A unimodal Allee map is thus a unimodal map with tree fixed points, a zero fixed point, a small positive fixed point, called threshold point, and a bigger positive fixed point, called the carrying capacity. In this paper the properties and stability of the three fixed points are studied in the setting of nonautonomous periodic dynamical systems or difference equations. Finally we investigate the bifurcation of …
Towards A Theory Of Periodic Difference Equations And Its Application To Population Dynamics, Saber Elaydi, Rafael Luis, Henrique Oliveira
Towards A Theory Of Periodic Difference Equations And Its Application To Population Dynamics, Saber Elaydi, Rafael Luis, Henrique Oliveira
Saber Elaydi
This survey contains the most updated results on the dynamics of periodic difference equations or discrete dynamical systems this time. Our focus will be on stability theory, bifurcation theory, and on the effect of periodic forcing on the welfare of the population (attenuance versus resonance). Moreover, the survey alludes to two more types of dynamical systems, namely, almost periodic difference equations and stochastic di®erence equations.
Bifurcation And Invariant Manifolds Of The Logistic Competition Model, Malgorzata Guzowska, Rafael Luis, Saber Elaydi
Bifurcation And Invariant Manifolds Of The Logistic Competition Model, Malgorzata Guzowska, Rafael Luis, Saber Elaydi
Saber Elaydi
In this paper we study a new logistic competition model. We will investigate stability and bifurcation of the model. In particular, we compute the invariant manifolds, including the important center manifolds, and study their bifurcation. Saddle-node and period doubling bifurcation route to chaos is exhibited via numerical simulations.
Spontaneous Oscillations In Simple Fluid Networks, Nathaniel Karst, Brian Storey, John Geddes
Spontaneous Oscillations In Simple Fluid Networks, Nathaniel Karst, Brian Storey, John Geddes
Brian Storey
Nonlinear phenomena including multiple equilibria and spontaneous oscillations are common in fluid networks containing either multiple phases or constituents. In many systems, such behavior might be attributed to the complicated geometry of the network, the complex rheology of the constituent fluids, or, in the case of microvascular blood flow, biological control. In this paper we investigate two examples of a simple three-node fluid network containing two miscible Newtonian fluids of differing viscosities, the first modeling microvascular blood flow and the second modeling stratified laminar flow. We use a combination of analytic and numerical techniques to identify and track saddle-node and …
Spontaneous Oscillations In Simple Fluid Networks, Nathaniel Karst, Brian Storey, John Geddes
Spontaneous Oscillations In Simple Fluid Networks, Nathaniel Karst, Brian Storey, John Geddes
John B. Geddes
Nonlinear phenomena including multiple equilibria and spontaneous oscillations are common in fluid networks containing either multiple phases or constituents. In many systems, such behavior might be attributed to the complicated geometry of the network, the complex rheology of the constituent fluids, or, in the case of microvascular blood flow, biological control. In this paper we investigate two examples of a simple three-node fluid network containing two miscible Newtonian fluids of differing viscosities, the first modeling microvascular blood flow and the second modeling stratified laminar flow. We use a combination of analytic and numerical techniques to identify and track saddle-node and …
Towards A Theory Of Periodic Difference Equations And Its Application To Population Dynamics, Saber Elaydi, Rafael Luis, Henrique Oliveira
Towards A Theory Of Periodic Difference Equations And Its Application To Population Dynamics, Saber Elaydi, Rafael Luis, Henrique Oliveira
Saber Elaydi
This survey contains the most updated results on the dynamics of periodic difference equations or discrete dynamical systems this time. Our focus will be on stability theory, bifurcation theory, and on the effect of periodic forcing on the welfare of the population (attenuance versus resonance). Moreover, the survey alludes to two more types of dynamical systems, namely, almost periodic difference equations and stochastic di®erence equations.