Related papers: From Logistic Growth to Exponential Growth in a Po…
The impact of environmental variability on population size growth rate in dynamic models is a recurrent issue in the theoretical ecology literature. In the scalar case, R. Lande pointed out that results are ambiguous depending on whether…
The logistic growth model is a classical framework for describing constrained growth phenomena, widely applied in areas such as population dynamics, epidemiology, and resource management. This study presents a generalized extension using…
In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We…
We consider long-time behavior of dynamical systems perturbed by a small noise. Under certain conditions, a slow component of such a motion, which is most important for long- time evolution, can be described as a motion on the cone of…
We demonstrate by mathematical analysis and systematic computer simulations that redistribution can lead to sustainable growth in a society. The human capital dynamics of each agent is described by a stochastic multiplicative process which,…
We analyze the fluctuation of the number of individuals when two competing species, beginning with a few initial individuals, are submitted to a logistic growth. We show that when the total number of individuals reaches the carrying…
The presence of chaos in classical Hamiltonian systems is witnessed by its maximal Lyapunov exponent, that quantifies the instability of motion through the exponential growth of indicators such as the trace of the stability matrix or the…
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
Mathematical models are vital interpretive and predictive tools used to assist in the understanding of cell migration. There are typically two approaches to modelling cell migration: either micro-scale, discrete or macro-scale, continuum.…
We consider a macroscopic model for the growth of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Assuming a power-law relation between the mechanical pressure and the cell density, the model can…
We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics.…
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…
We introduce a model of randomly connected neural populations and study its dynamics by means of the dynamical mean-field theory and simulations. Our analysis uncovers a rich phase diagram, featuring high- and low-dimensional chaotic…
In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…
We explore a class of hybrid (piecewise deterministic) systems characterized by a large number of individuals inhabiting an environment whose state is described by a set of continuous variables. We use analytical and numerical methods from…
The diffusion of ideas is often closely connected to the creation and diffusion of knowledge and to the technological evolution of society. Because of this, knowledge creation, exchange and its subsequent transformation into innovations for…
Following some recent works, we investigate the problem of optimising the total population size for logistic diffusive models with respect to resources distributions. Using the spatially heterogeneous Fisher-KPP equation, we obtain a…
Many systems in nature and laboratories are far from equilibrium and exhibit significant fluctuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability…
Two powerful and complementary experimental approaches are commonly used to study the cell cycle and cell biology: One class of experiments characterizes the statistics (or demographics) of an unsynchronized exponentially-growing…
We present a stochastic model of gait rhythm dynamics, based on transitions between different ``neural centers'', that reproduces distinctive statistical properties of normal human walking. By tuning one model parameter, the hopping range,…