Related papers: From Logistic Growth to Exponential Growth in a Po…
Consider a species whose population density solves the steady diffusive logistic equation in a heterogeneous environment modeled with the help of a spatially non constant coefficient standing for a resources distribution in a given box. We…
Using linearized elasticity as a convenient mechanical framework, we show that volumetric growth can be formulated as an optimization-driven process in which the growth tensor is determined implicitly by constrained optimization rather than…
The population protocol model describes collections of distributed agents that interact in pairs to solve a common task. We consider a dynamic variant of this prominent model, where we assume that an adversary may change the population size…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…
Many analyses of resource-allocation problems employ simplistic models of the population. Using the example of a resource-allocation problem of Marecek et al. [arXiv:1406.7639], we introduce rather a general behavioural model, where the…
The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system…
In this study, we couple a population dynamics model with a model for optimal foraging to study the interdependence between individual-level cost-benefits and population-scale dynamics. Specifically, we study the logistic growth model,…
The effect of stochasticity, in the form of Gaussian white noise, in a predator-prey model with two distinct time-scales is presented. A supercritical singular Hopf bifurcation yields a Type II excitability in the deterministic model. We…
The growth of complex populations, such as microbial communities, forests, and cities, occurs over vastly different spatial and temporal scales. Although research in different fields has developed detailed, system-specific models to…
This paper presents a theoretical study on the influence of a discrete element in the nonlinear dynamics of a continuous mechanical system subject to randomness in the model parameters. This system is composed by an elastic bar, attached to…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
In 2006 (J. Differential Equ.), Lou proved that, once the intrinsic growth rate $r$ in the logistic model is proportional to the spatially heterogeneous carrying capacity $K$ ($r=K^1$), the total population under the regular diffusion…
A new stochastic control problem of population dynamics under partial observation is formulated and analyzed both mathematically and numerically, with an emphasis on environmental and ecological problems. The decision-maker can only…
In this article, we give an in-depth analysis of the problem of optimising the total population size for a standard logistic-diffusive model. This optimisation problem stems from the study of spatial ecology and amounts to the following…
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…
We study a stochastic model for tumor cell growth with both multiplicative and additive colored noise as well as a non-zero cross-correlations in between. Whereas the death rate within the logistic model is altered by a deterministic term…
We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by…
We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition…
This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master…