Related papers: Phase Space Formulation of Population Dynamics in …
Concise, accurate descriptions of physical systems through their conserved quantities abound in the natural sciences. In data science, however, current research often focuses on regression problems, without routinely incorporating…
We present a Hamiltonian approach for the wellknown Eigen model of the Darwin selection dynamics. Hamiltonization is carried out by means of the embedding of the population variable space, describing behavior of the system, into the space…
We carry out mathematical analyses, {\em \`{a} la} Helmholtz's and Boltzmann's 1884 studies of monocyclic Newtonian dynamics, for the Lotka-Volterra (LV) equation exhibiting predator-prey oscillations. In doing so a novel "thermodynamic…
In this work, we consider a system of differential equations modeling the dynamics of some populations of preys and predators, moving in space according to rapidly oscillating time-dependent transport terms, and interacting with each other…
It has been recently argued that near-integrable nonautonomous one-degree-of-freedom Hamiltonian systems are constrained by KAM theory even when the time-dependent (nonintegrable) part of the Hamiltonian is given in the form of a…
Simultaneous deterministic and weakly stochastic dynamics of multiple populations described by a large system of ODE's is considered in the phase space of population sizes and ODE's parameters. We show that many practically interesting…
Population dynamics deals with the collective phenomena of living organisms, and it has attracted much attention since it is expected to explain how not only living organisms but also human beings have been adapted to varying environments.…
Human society is an open system that evolves by coupling with various known and unknown (energy) fluxes. How do these dynamics precisely unfold? Energetics may provide further insights. We expand on Navier Stokes' approach to study…
In this paper we propose the time-dependent Hamiltonian form of human biomechanics, as a sequel to our previous work in time-dependent Lagrangian biomechanics [1]. Starting with the Covariant Force Law, we first develop autonomous…
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…
Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density. A whole family of simple and popular…
A striking feature of the marine ecosystem is the regularity in its size spectrum: the abundance of organisms as a function of their weight approximately follows a power law over almost ten orders of magnitude. We interpret this as evidence…
In any ecosystem, the conditions of the environment and the characteristics of the species that inhabit it are entangled, co-evolving in space and time. We introduce a model that couples active agents with a dynamic environment, interpreted…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
This study investigates the potential for biological systems to be governed by a variational principle, suggesting that such systems may evolve to minimize or optimize specific quantities. To explore this idea, we focus on identifying…
We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated…
Momentum-space representation renders an interesting perspective to theory of large fluctuations in populations undergoing Markovian stochastic gain-loss processes. This representation is obtained when the master equation for the…
The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional…