Related papers: Exactly solvable dynamics of the Eigen and the Cro…
We study the asymptotic behavior of an integro-dierential equation describing the evolutionary adaptation of a population structured by a phenotypic trait. The model takes into account mutation, selection, horizontal gene transfer and…
Using the Hamilton-Jacobi equation approach to study genomes of length $L$, we obtain 1/L corrections for the steady state population distributions and mean fitness functions for horizontal gene transfer model, as well as for the diploid…
In this work, we characterize the solution of a system of elliptic integro-differential equations describing a phenotypically structured population subject to mutation, selection and migration between two habitats. Assuming that the effects…
In this note, we characterize the solution of a system of elliptic integro-differential equations describing a phe-notypically structured population subject to mutation, selection and migration. Generalizing an approach based on…
A few quasi-exactly solvable models are studied within the quantum Hamilton-Jacobi formalism. By assuming a simple singularity structure of the quantum momentum function, we show that the exact quantization condition leads to the condition…
We map Eigen model of biological evolution [Naturwissenschaften {\bf 58}, 465 (1971)] into a one-dimensional quantum spin model with non-Hermitean Hamiltonian. Based on such a connection, we derive exact relaxation periods for the Eigen…
In this paper, we investigate the asymptotic behavior of individual-based models describing the evolution of a population structured by a real trait, subject to selection and mutation. We consider two different sets of assumptions: first,…
We study a mathematical model describing the growth process of a population structured by age and a phenotypical trait, subject to aging, competition between individuals and rare mutations. Our goals are to describe the asymptotic behaviour…
The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the…
We considered a {multi-block} molecular model of biological evolution, in which fitness is a function of the mean types of alleles located at different parts (blocks) of the genome. We formulated an infinite population model with selection…
The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. First, we recast the model as a singularly perturbed dynamics which we embed in a family of controlled…
We develop a discrete analogue of Hamilton-Jacobi theory in the framework of discrete Hamiltonian mechanics. The resulting discrete Hamilton-Jacobi equation is discrete only in time. We describe a discrete analogue of Jacobi's solution and…
In this paper, we study an integro-differential equation which describes the evolutionary dynamics of a population structured by a phenotypic trait. This population undergoes asexual reproduction, competition, selection, and mutation. We…
The rarely used Hamilton-Jacobi equation has been utilized as an elegant way to find the trajectories of mechanical systems and to derive symplectic maps. Further, the exact solution in kick approximation of Hamilton's equations of motion…
Hybrid dynamical systems with nonlinear dynamics are one of the most general modeling tools for representing robotic systems, especially contact-rich systems. However, providing guarantees regarding the safety or performance of nonlinear…
We study quantitative large-time averages for Hamilton--Jacobi equations in a dynamic random environment that is stationary ergodic and has unit-range dependence in time. Our motivation comes from stochastic growth models related to the…
We discuss an extension of the Hamilton-Jacobi theory to nonholonomic mechanics with a particular interest in its application to exactly integrating the equations of motion. We give an intrinsic proof of a nonholonomic analogue of the…
Real-world autonomous systems often employ probabilistic predictive models of human behavior during planning to reason about their future motion. Since accurately modeling human behavior a priori is challenging, such models are often…
We present a partial-differential-equation-based optimal path-planning framework for curvature constrained motion, with application to vehicles in 2- and 3-spatial-dimensions. This formulation relies on optimal control theory, dynamic…
By using the effective Hamiltonian approach, we present a self-consistent framework for the analysis of geometric phases and dynamically stable decoherence-free subspaces in open systems. Comparisons to the earlier works are made. This…