1,721,053 research outputs found
On some dynamical features of the complete Moran model for neutral evolution in the presence of mutations
Full text linkWe present a version of the classical Moran model, in which mutations aretaken into account; the possibility of mutations was introduced by Moran in hisseminal paper, but it is more often overlooked in discussing the Moran model.For this model, fixation is prevented by mutation, and we have an ergodicMarkov process; the equilibrium distribution for such a process was determinedby Moran. The problems we consider in this paper are those of first hittingeither one of the ``pure'' (uniform population) states, depending on theinitial state; and that of first hitting times. The presence of mutations leadsto a nonlinear dependence of the hitting probabilities on the initial state,and to a larger mean hitting time compared to the mutation-free process (inwhich case hitting corresponds to fixation of one of the alleles).Comment: 22 pages, 8 figure
Asymptotic scaling in a model class of anomalous reaction-diffusion equations
No full textWe analyze asymptotic scaling properties of a model class of anomalous reaction-diffusion (ARD) equations. Numerical experiments show that solutions to these have, for large t, well defined scaling properties. We suggest a general framework to analyze asymptotic symmetry properties; this provides an analytical explanation of the observed asymptotic scaling properties for the considered ARD equations
Symmetry of the isotropic Ornstein-Uhlenbeck process in a force field
Full text linkWe classify simple symmetries for an Ornstein-Uhlenbeck process, describing a particle in an external force field f(x). It turns out that for sufficiently regular (in a sense to be defined) forces there are nontrivial symmetries only if f(x) is at most linear. We fully discuss the isotropic case, while for the non-isotropic we only deal with a generic situation (defined in detail in the text)
Dimension Increase and Splitting for Poincaré-Dulac Normal Forms
No full textIntegration of nonlinear dynamical systems is usually seen as associated to a symmetry reduction, e.g. via momentum map. In Lax integrable systems, as pointed out by Kazhdan, Kostant and Sternberg in discussing the Calogero system, one proceeds in the opposite way, enlarging the nonlinear system to a system of greater dimension. We discuss how this approach is also fruitful in studying non integrable systems, focusing on systems in normal form
Symmetry classification of scalar autonomous Ito stochastic differential equations with simple noise
Full text linkIt is known that knowledge of a symmetry of a scalar Ito stochastic differential equations leads, thanks to the Kozlov substitution, to its integration. In the present paper we provide a classification of scalar autonomous Ito stochastic differential equations with simple noise possessing symmetries; here ``simple noise'' means the noise coefficient is of the form \s (x,t) = s x^k, with and real constants. Such equations can be taken to a standard form via a well known transformation; for such standard forms we also provide the integration of the symmetric equations. Our work extends previous classifications in that it also considers recently introduced types of symmetries, in particular standard random symmetries, not considered in those
Integrable Ito equations and properties of the associated Fokker-Planck equations
Full text linkIn a recent paper we have classified scalar Ito equations which admits a
standard symmetry; these are also directly integrable by the Kozlov
substitution. In the present work, we consider the diffusion (Fokker-Planck)
equations associated to such symmetric Ito equations.Comment: 24 pages, no figure
Integrable Ito equations with multiple noises
Full text linkThe classification of scalar Ito equations with a single noise source which admit a so called standard symmetry and hence are -- by the Kozlov construction -- integrable is by now complete. In this paper we study the situation, occurring in physical as well as biological applications, where there are two independent noise sources. We determine all such autonomous Ito equations admitting a standard symmetry; we then integrate them by means of the Kozlov construction. We also consider the case of three or more independent noises, showing no standard symmetry is present
On the geometry of lambda-symmetries and PDE reduction
No full textWe give a geometrical characterization of λ-prolongations of vector fields, and
hence of λ-symmetries of ODEs. This allows an extension to the case of PDEs
and systems of PDEs; in this context the central object is a horizontal 1-form μ,
and we speak of μ-prolongations of vector fields and μ-symmetries of PDEs.
We show that these are as good as standard symmetries in providing symmetry
reduction of PDEs and systems, and explicit invariant solutions
Maximal degree variational principles and Liouville dynamics
No full textAbstractLet M be smooth n-dimensional manifold, fibered over a k-dimensional submanifold B as π:M→B, and ϑ∈Λk(M); one can consider the functional on sections φ of the bundle π defined by ∫Dφ∗(ϑ), with D a domain in B. We show that for k=n−2 the variational principle based on this functional identifies a unique (up to multiplication by a smooth function) nontrivial vector field in M, i.e., a system of ODEs. Conversely, any vector field X on M satisfying X⌟dϑ=0 for some ϑ∈Λn−2(M) admits such a variational characterization. We consider the general case, and also the particular case M=P×R where one of the variables (the time) has a distinguished role; in this case our results imply that any Liouville (volume-preserving) vector field on the phase space P admits a variational principle of the kind considered here
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