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Articles 1 - 14 of 14
Full-Text Articles in Physical Sciences and Mathematics
Efficient Simulation Of A Simple Evolutionary System, Mahendra Duwal Shrestha
Efficient Simulation Of A Simple Evolutionary System, Mahendra Duwal Shrestha
Masters Theses
An infinite population model is considered for diploid evolution under the influence of crossing over and mutation. The evolution equations show how Vose’s haploid model for Genetic Algorithms extends to the diploid case, thereby making feasible simulations which otherwise would require excessive resources. This is illustrated through computations confirming the convergence of finite diploid population short-term behaviour to the behaviour predicted by the infinite diploid model. The results show the distance between finite and infinite population evolutionary trajectories can decrease in practice like the reciprocal of the square root of population size.
Under necessary and sufficient conditions (NS) concerning mutation …
An Extension Of Sharkovsky’S Theorem To Periodic Difference Equations, Ziyad Alsharawi, James Angelos, Saber Elaydi, Leela Rakesh
An Extension Of Sharkovsky’S Theorem To Periodic Difference Equations, Ziyad Alsharawi, James Angelos, Saber Elaydi, Leela Rakesh
Saber Elaydi
We present an extension of Sharkovsky’s Theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric cycle with or without stability properties.
Existence And Stability Of Periodic Orbits Of Periodic Difference Equations With Delays, Ziyad Alsharawi, James Angelos, Saber Elaydi
Existence And Stability Of Periodic Orbits Of Periodic Difference Equations With Delays, Ziyad Alsharawi, James Angelos, Saber Elaydi
Saber Elaydi
In this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays xn = f(n−1, xn−k). We show that the periodic orbits of this equation depend on the periodic orbits of p autonomous equations when p divides k. When p is not a divisor of k, the periodic orbits depend on the periodic orbits of gcd(p, k) nonautonomous p gcd(p,k) - periodic difference equations. We give formulas for calculating the number of different periodic orbits under certain conditions. In addition, when p and k are relatively prime integers, we introduce what we call …
Pt-Symmetric Dimer In A Generalized Model Of Coupled Nonlinear Oscillators, Jesús Cuevas–Maraver, Avinash Khare, Panayotis G. Kevrekidis, Haitao Xu, Avadh Saxena
Pt-Symmetric Dimer In A Generalized Model Of Coupled Nonlinear Oscillators, Jesús Cuevas–Maraver, Avinash Khare, Panayotis G. Kevrekidis, Haitao Xu, Avadh Saxena
Mathematics and Statistics Department Faculty Publication Series
Abstract In the present work, we explore the case of a general PT -symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schrödinger type dimer. In the latter context, the stationary solutions and their stability are identified numerically but also wherever possible analytically. Solutions stemming from both symmetric and anti-symmetric special limits are identified. A number of special cases are explored regarding the ratio of coefficients of nonlinearity between oscillators over the intrinsic one …
A Generalized Cholera Model And Epidemic-Endemic Analysis, Jin Wang, Shu Liao
A Generalized Cholera Model And Epidemic-Endemic Analysis, Jin Wang, Shu Liao
Mathematics & Statistics Faculty Publications
The transmission of cholera involves both human-to-human and environment-to-human pathways that complicate its dynamics. In this paper, we present a new and unified deterministic model that incorporates a general incidence rate and a general formulation of the pathogen concentration to analyse the dynamics of cholera. Particularly, this work unifies many existing cholera models proposed by different authors. We conduct equilibrium analysis to carefully study the complex epidemic and endemic behaviour of the disease. Our results show that despite the incorporation of the environmental component, there exists a forward transcritical bifurcation at R0 = 1 for the combined human-environment epidemiological …
Analytic Construction Of Periodic Orbits In The Restricted Three-Body Problem, Mohammed A. Ghazy
Analytic Construction Of Periodic Orbits In The Restricted Three-Body Problem, Mohammed A. Ghazy
Mechanical & Aerospace Engineering Theses & Dissertations
This dissertation explores the analytical solution properties surrounding a nominal periodic orbit in two different planes, the plane of motion of the two primaries and a plane perpendicular to the line joining the two primaries, in the circular restricted three-body problem. Assuming motion can be maintained in the plane and motion of the third body is circular, Jacobi's integral equation can be analytically integrated, yielding a closed-form expression for the period and path expressed with elliptic integral and elliptic function theory. In this case, the third body traverses a circular path with nonuniform speed. In a strict sense, the in-plane …
Existence And Stability Of Periodic Orbits Of Periodic Difference Equations With Delays, Ziyad Alsharawi, James Angelos, Saber Elaydi
Existence And Stability Of Periodic Orbits Of Periodic Difference Equations With Delays, Ziyad Alsharawi, James Angelos, Saber Elaydi
Mathematics Faculty Research
In this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays xn = ƒ(n−1, xn−k). We show that the periodic orbits of this equation depend on the periodic orbits of p autonomous equations when p divides k. When p is not a divisor of k, the periodic orbits depend on the periodic orbits of gcd(p, k) nonautonomous p/gcd(p,k) - periodic difference equations. We give formulas for calculating the number of different periodic orbits under …
Simple Braids For Surface Homeomorphisms, Kamlesh Parwani
Simple Braids For Surface Homeomorphisms, Kamlesh Parwani
Kamlesh Parwani
Let S be a compact, oriented surface with negative Euler characteristic and f:S→S be a homeomorphism isotopic to the identity. If there exists a periodic orbit with a non-zero rotation vector (p→,q), then there exists a simple braid with the same rotation vector.
Simple Braids For Surface Homeomorphisms, Kamlesh Parwani
Simple Braids For Surface Homeomorphisms, Kamlesh Parwani
Faculty Research and Creative Activity
Let S be a compact, oriented surface with negative Euler characteristic and f:S→S be a homeomorphism isotopic to the identity. If there exists a periodic orbit with a non-zero rotation vector (p→,q), then there exists a simple braid with the same rotation vector.
Simple Braids For Surface Homeomorphisms, Kamlesh Parwani
Simple Braids For Surface Homeomorphisms, Kamlesh Parwani
Faculty Research and Creative Activity
Let S be a compact, oriented surface with negative Euler characteristic and f:S→S be a homeomorphism isotopic to the identity. If there exists a periodic orbit with a non-zero rotation vector (p→,q), then there exists a simple braid with the same rotation vector.
An Extension Of Sharkovsky’S Theorem To Periodic Difference Equations, Ziyad Alsharawi, James Angelos, Saber Elaydi, Leela Rakesh
An Extension Of Sharkovsky’S Theorem To Periodic Difference Equations, Ziyad Alsharawi, James Angelos, Saber Elaydi, Leela Rakesh
Mathematics Faculty Research
We present an extension of Sharkovsky’s Theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric cycle with or without stability properties.
Robustly Transitive Sets And Heterodimensional Cycles, Christian Bonatti, Lorenzo J. Díaz, Enrique R. Pujals, Jorge Rocha
Robustly Transitive Sets And Heterodimensional Cycles, Christian Bonatti, Lorenzo J. Díaz, Enrique R. Pujals, Jorge Rocha
Publications and Research
It is known that all non-hyperbolic robustly transitive sets Λφ have a dominated splitting and, generically, contain periodic points of different indices. We show that, for a C1-dense open subset of diffeomorphisms φ, the indices of periodic points in a robust transitive set Λφ form an interval in ℕ. We also prove that the homoclinic classes of two periodic points in Λφ are robustly equal. Finally, we describe what sort of homoclinic tangencies may appear in Λφ by studying its dominated splittings.
A Zeta Function For Flows With Positive Templates, Michael C. Sullivan
A Zeta Function For Flows With Positive Templates, Michael C. Sullivan
Articles and Preprints
A zeta function for a map f : M → M is a device for counting periodic orbits. For a topological flow however, there is not a clear meaning to the period of a closed orbit. We circumvent this for flows which have positive templates by counting the “twists” in the stable manifolds of the periodic orbits.
Composite Knots In The Figure-8 Knot Complement Can Have Any Number Of Prime Factors, Michael C. Sullivan
Composite Knots In The Figure-8 Knot Complement Can Have Any Number Of Prime Factors, Michael C. Sullivan
Articles and Preprints
We study an Anosov flow Фt in S3 – {figure-8 knots}. Birman and Williams conjectured that the knot types of the periodic orbits of this flow could have at most two prime factors. Below, we give a geometric method for constructing knots in this flow with any number of prime factors.