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Mathematics

2011

Series

Mathematics Faculty Research

Articles 1 - 5 of 5

Full-Text Articles in Physical Sciences and Mathematics

Bifurcation And Invariant Manifolds Of The Logistic Competition Model, M. Guzowska, Rafael Luís, Saber Elaydi Dec 2011

Bifurcation And Invariant Manifolds Of The Logistic Competition Model, M. Guzowska, Rafael Luís, Saber Elaydi

Mathematics Faculty Research

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.

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A Generalization Of The Fujisawa–Kuh Global Inversion Theorem, M. Radulescu, S. Radulescu, Eduardo C. Balreira Oct 2011

A Generalization Of The Fujisawa–Kuh Global Inversion Theorem, M. Radulescu, S. Radulescu, Eduardo C. Balreira

Mathematics Faculty Research

We discuss the problem of global invertibility of nonlinear maps defined on the finitedimensional Euclidean space via differential tests. We provide a generalization of theFujisawa-Kuh global inversion theorem and introduce a generalized ratio conditionwhich detects when the pre-image of a certain class of linear manifolds is non-emptyand connected. In particular, we provide conditions that also detect global injectivity.

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Budding Yeast, Branching Processes, And Generalized Fibonacci Numbers, Peter Olofsson, Ryan C. Daileda Jun 2011

Budding Yeast, Branching Processes, And Generalized Fibonacci Numbers, Peter Olofsson, Ryan C. Daileda

Mathematics Faculty Research

A real-world application of branching processes to a problem in cell biology where the generalized Fibonacci numbers known as k-nacci numbers play a crucial role is described. The k-nacci sequence is used to obtain asymptotics, computational formulas, and to justify certain practical simplifications. Along the way, an explicit formula for the sum of k-nacci numbers is established.

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Towards A Theory Of Periodic Difference Equations And Its Application To Population Dynamics, Saber Elaydi, Rafael Luís, Henrique Oliveira Jan 2011

Towards A Theory Of Periodic Difference Equations And Its Application To Population Dynamics, Saber Elaydi, Rafael Luís, Henrique Oliveira

Mathematics Faculty Research

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.

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Reverse Mathematics And Uniformity In Proofs Without Excluded Middle, Jeffry L. Hirst, Carl Mummert Jan 2011

Reverse Mathematics And Uniformity In Proofs Without Excluded Middle, Jeffry L. Hirst, Carl Mummert

Mathematics Faculty Research

We show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak classical subsystems. In particular, if a \Pi^1_2 sentence of a certain form is provable using E-HAω along with the axiom of choice and an independence of premise principle, the sequential form of the statement is provable in the classical system RCA. We obtain this and similar results using applications of modified realizability and the Dialectica interpretation. These results allow us to use techniques of classical reverse mathematics to demonstrate the unprovability of several mathematical principles …

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