The dynamical system arising from the problem of billiards is a classical example where the theory of twist maps can be applied. In the case of an elliptic billiard table, the corresponding twist map is integrable and...
The dynamical system arising from the problem of billiards is a classical example where the theory of twist maps can be applied. In the case of an elliptic billiard table, the corresponding twist map is integrable and has a saddle connection between two hyperbolic period two points. Using a discrete analog to the Melnikov method, we are able to show that this saddle connection can be deformed into a transversal heteroclinic connection under certain analytic perturbations of the table. From the formulas that we get, we can show that the splitting of the separatrices is exponentially small as a function of the eccentricity of the original unperturbed elliptic table. In addition, we also include a characterization of the period two periodic points for any billiard table.
In this paper we are concerned with the dynamics of noninvertible transformations of the plane. Three examples are explored and possibly a new bifurcation, or ''eruption,'' is described. A fundamental ...
In this paper we are concerned with the dynamics of noninvertible transformations of the plane. Three examples are explored and possibly a new bifurcation, or ''eruption,'' is described. A fundamental role is played by the interactions of fixed paints and singular curves. Other critical elements in the phase space include periodic points and an invariant line. The dynamics along the invariant line, in two of the examples, reduces to the one-dimensional Newton's method which is conjugate to a degree two ratoional map. We also determine, computationally, the characteristic exponents for all of the systems. An unexpected coincidence is that the parameter range where the invariant line becomes neutrally stable, as measured by a zero Lyapunov exponent, coincides with the merging of a periodic point with a point on a singular curve. (C) 1996 American Institute of Physics.
We work with symplectic diffeomorphisms of the n-annulus A(n) = T*(R-n/Z(n)). Using the variational approach of Aubry and Mather, we are able to give a local description of the stable (and unstable) manifold for a hyp...
We work with symplectic diffeomorphisms of the n-annulus A(n) = T*(R-n/Z(n)). Using the variational approach of Aubry and Mather, we are able to give a local description of the stable (and unstable) manifold for a hyperbolic fixed point. We use this in order to get a Melnikov-like formula for exact symplectic twist maps. This formula involves an infinite series that could be computed in some specific cases. We apply our formula to prove the existence of heteroclinic orbits for a family of twist maps in R-4.
We present a simple algorithm for the factored polynomial (Finite Impulse Response, FIR) approximation of rational (Infinite Impulse Response, IIR) filters which may be used to construct inverse filters. When applied ...
We present a simple algorithm for the factored polynomial (Finite Impulse Response, FIR) approximation of rational (Infinite Impulse Response, IIR) filters which may be used to construct inverse filters. When applied to quadrature mirror filters, our approach yields a simple way of generating an efficient FIR filter bank which inherits the properties of IIR filter bank with any desired accuracy. (C) 1995 Academic Press, Inc.
The Benjamin-Ono equation is shown to admit a two-parameter family of Miura transformations, leading to a proof that the equation has an infinite number of conserved densities. Linearized equations are derived from a ...
The Benjamin-Ono equation is shown to admit a two-parameter family of Miura transformations, leading to a proof that the equation has an infinite number of conserved densities. Linearized equations are derived from a special case of the transformation.
A class of Hamiltonian systems derived from nonstandard Poisson brackets are investigated. For each system a conserved quantity is constructed that depends only upon the definition of the Poisson bracket. The quantum ...
A class of Hamiltonian systems derived from nonstandard Poisson brackets are investigated. For each system a conserved quantity is constructed that depends only upon the definition of the Poisson bracket. The quantum theory for these systems is sketched and classical and quantum ''blowup'' phenomena are compared.
An intelligent Levenberg-Marquardt Technique (LMT) with artificial neural network (ANN) backpropagation (BP) has been used to analyze the thermal heat and mass transfer of unsteady magnetohydrodynamics (MHD) thin film...
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An intelligent Levenberg-Marquardt Technique (LMT) with artificial neural network (ANN) backpropagation (BP) has been used to analyze the thermal heat and mass transfer of unsteady magnetohydrodynamics (MHD) thin film Maxwell fluid flow in a porous inclined sheet with an emphasis on the influence of electro-osmosis. The activation energy, chemical reaction, mixed convection, melting heat, joule heating, nonlinear thermal radiation, variable thermal conductivity and thermal source/sink effect are taken into account for transport expressions. Appropriate similarity transformations were used to translate partial differential equations (PDEs) into ordinary differential equations (ODEs). After that, the built-in MATLAB BVP4C method was used for a data set assessed using the LMT-ANN strategy to solve these ODEs. The physical significance of the designed parameters is thoroughly discussed in both tabular and graphical form. The observed R -squared value is 1, and the mean square error up to 10 − 15 demonstrates the LMT-ANN's precise and accurate computing capability. The model’s validity is also confirmed by the strong agreement between the obtained predicted findings and numerical results, which shows a high degree of accuracy within the range of 10 − 8 to 10 − 11 . It was revealed that radiative heat considerably increases surface heat energy through accumulation, improving heat transfer qualities, whereas fluid temperature is raised by Joule dissipation, variable thermal conductivity, and heat source. Electro-osmosis and magnetic fields reduce fluid velocity by generating opposing forces that resist the flow. This problem works best in microscale fluid transport systems and drilling operations, where magnetic and electro-osmotic control are crucial. These systems include micro-electromechanical systems, lab-on-a-chip devices, porous geological formations, and thin film coating technologies.
A new rotation symmetry for steady Hele-Shaw flows is reported. In the case when surface tension is neglected, it is shown that if a curve L moving with constant velocity U is a solution to the Hele-Shaw problem, then...
A new rotation symmetry for steady Hele-Shaw flows is reported. In the case when surface tension is neglected, it is shown that if a curve L moving with constant velocity U is a solution to the Hele-Shaw problem, then the curve L obtained from a rotation of L about its center by an arbitrary angle is also a solution with the same velocity U. Similar results hold for the case with surface tension if and only if the Schwarz function of the curve L is regular in the fluid region and at most a linear function at infinity. Several examples in which this principle is used to generate new solutions to the problem are also discussed.
作者：
CUSHING, JMDepartment of Mathematics
Interdisciplinary Program in Applied Mathematics Building 89 University of Arizona Tucson Arizona 85721 USA
A size-structured model for the dynamics of a cannibalistic population is derived under the assumption that cannibals (successfully) attack only smaller bodied victims, as is generally the case in the biological world...
A size-structured model for the dynamics of a cannibalistic population is derived under the assumption that cannibals (successfully) attack only smaller bodied victims, as is generally the case in the biological world. In addition to the resulting size-dependent death rate, the model incorporates the positive feedback mechanism resulting from the added resource energy obtained by the cannibal from the consumption of the victim. From the nonlinear partial integro-differential equation model, it is shown how to obtain a complete analysis of the global dynamics of the total population biomass. This analysis yields many dynamical features that have been attributed to cannibalism in the literature, including density self-regulation, a “life-boat strategy” phenomenon by which a population avoids extinction by practicing cannibalism under circumstances when it would otherwise go extinct, and multiple stable positive equilibrium states and hysteresis.
作者：
CUSHING, JMDepartment of Mathematics
Interdisciplinary Program in Applied Mathematics Building 89 University of Arizona Tucson Arizona 85721 USA
This paper deals with the problem of relating physiological properties of individual organisms to the dynamics at the total population level. A general nonlinear matrix difference equation is described which accounts ...
This paper deals with the problem of relating physiological properties of individual organisms to the dynamics at the total population level. A general nonlinear matrix difference equation is described which accounts for the dynamics of stage-structured populations under the assumption that individuals in the populations can be placed into well defined descriptive stages. Density feedback is modeled through an assumption that (stage-specific) fertilities and transitions are proportional to a resource uptake functional which is dependent upon a total weighted population size. It is shown how, if stage-specific differences in mortality are insignificant compared to stage-specific differences in fertility and inter-stage transitions, a nonlinear version of the strong ergodic theorem of demography mathematically separates the population level dynamics from the dynamics of the stage distribution vector, which is shown to stabilize independently of the population level dynamics. The nonlinear dynamics at the population level are governed by a key parameter π that encapsulates the stage-specific parameters and thereby affords a means by which population level dynamics can be linked to properties of individual organisms. The method is applied to a community of stagestructured populations competing for a common limiting resource, and it is seen how the parameter π determines the competitively superior species. An example of size structured competitors illustrates how the method can relate the competitive success of a species to such size-specific properties as resource conversion efficiencies and allocation fractions for individual growth and reproduction, largest adult body size, and size at birth and maturation.
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