Search results for "Nonlinear system"
showing 10 items of 1446 documents
Generalized heat equation and transitions between different heat-transport regimes in narrow stripes
2019
Abstract In the framework of weakly nonlocal thermodynamic theory, in this paper we derive a nonlocal and nonlinear heat-transport equation beyond the Fourier law by means of thermodynamic considerations in agreement with the second law. The obtained equation describes the transitions among different heat-transport regimes. The stability of the solution of that equation is also analyzed in a special case.
Existence and uniqueness results for a nonlinear evolution equation arising in growing cell populations
2014
Abstract The present paper is concerned with a nonlinear initial–boundary value problem derived from a model introduced by Rotenberg (1983) describing the growth of a cell population. Each cell of this population is distinguished by two parameters: its degree of maturity μ and its maturation velocity v . At mitosis, the daughter cells and mother cells are related by a general reproduction rule. We prove existence and uniqueness results in the case where the total cross-section and the boundary conditions are depending on the total density of population. Local and nonlocal reproduction rules are discussed.
On determining unknown functions in differential systems, with an application to biological reactors.
2003
In this paper, we consider general nonlinear systems with observations, containing a (single) unknown function φ . We study the possibility to learn about this unknown function via the observations: if it is possible to determine the [values of the] unknown function from any experiment [on the set of states visited during the experiment], and for any arbitrary input function, on any time interval, we say that the system is “identifiable”. For systems without controls, we give a more or less complete picture of what happens for this identifiability property. This picture is very similar to the picture of the “observation theory” in [7]: Contrarily to the case of the observability property, i…
Nonlinear Relaxation in Population Dynamics
2001
We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random interaction between the species. We focus on the statistical properties of the asymptotic behaviour of the time integral of the i-th population and on the distribution of the population and of the local field.
EMERGING PROPERTIES IN POPULATION DYNAMICS WITH DIFFERENT TIME SCALES
1995
The aim of this work is to show that at the population level, emerging properties may occur as a result of the coupling between the fast micro-dynamics and the slow macrodynamics. We studied a prey-predator system with different time scales in a heterogeneous environment. A fast time scale is associated to the migration process on spatial patches and a slow time scale is associated to the growth and the interactions between the species. Preys go on the spatial patches on which some resources are located and can be caught by the predators on them. The efficiency of the predators to catch preys is patch-dependent. Preys can be more easily caught on some spatial patches than others. Perturbat…
An existence and uniqueness principle for a nonlinear version of the Lebowitz-Rubinow model with infinite maximum cycle length
2017
The present article deals with existence and uniqueness results for a nonlinear evolution initial-boundary value problem, which originates in an age-structured cell population model introduced by Lebowitz and Rubinow (1974) describing the growth of a cell population. Cells of this population are distinguished by age a and cycle length l. In our framework, daughter and mother cells are related by a general reproduction rule that covers all known biological ones. In this paper, the cycle length l is allowed to be infinite. This hypothesis introduces some mathematical difficulties. We consider both local and nonlocal boundary conditions.
Set Membership (In) Validation of nonlinear positive models for biological systems
2006
The complexity of biology needs quantitative tools in order to support and validate biologists intuition and traditional qualitative descriptions. In this paper, Nonlinear Positive models with constraints for biological systems are validated/invalidated in a worst-case deterministic setting. These models are usefull for the analysis of the DNA and RNA evolution and for the description of the population dynamics of viruses and bacteria. The conditional central estimate and the Uncertainty Intervals are determined in order to validate/invalidate the model. The effectiveness of the proposed procedure has been illustrated by means of simulation experiments.
Identification of Replicator Mutator models
2006
The complexity of biology literally calls for quantitative tools in order to support and validate biologists intuition and traditional qualitative descriptions. In this paper, the Replicator-Mutator models for Evolutionary Dynamics are validated/invalidated in a worst-case deterministic setting. These models analyze the DNA and RNA evolution or describe the population dynamics of viruses and bacteria. We identify the Fitness and the Replication Probability parameters of a genetic sequences, subject to a set of stringent constraints to have physical meaning and to guarantee positiveness. The conditional central estimate is determined in order to validate/invalidate the model. The effectivene…
The Measurement of Large Strains Using Electrical Resistance Strain Gages
2011
It is well known that in the range of large strains, the electrical resistance strain gages have a nonlinear behavior, that is the variation of electrical resistance is a nonlinear function of the strain applied to the strain gage, which means that the gage factor K is not constant. Also, the Wheatstone bridge has a nonlinear behavior at large strains. Usually the two nonlinearities have opposite effects, therefore the overall nonlinearity decreases. This article presents an overview of the behavior of strain gages subject to large strains and of the corrections to account for nonlinearities of both the strain gage and the Wheatstone bridge.
A Strategy for the Prediction of the Response of Hysteretic Systems: A Base for Capacity Assessment of Buildings under Seismic Load
2014
A statistical non linearization method is used to approximate systems modeled by the Bouc differential equa- tion and excited by a Gaussian white noise external load. To this aim restricted potential models (RPM) are used, which are suitable for an extended number of nonlinear problems as have been proved several times. Since the solution of RPM is known by the probabilistic point of view, all statistical characteristics can be derived at once with advantages by the computational point of view. Hence, this paper discusses the possibility to determine sets of parameters characterizing po- tential models that are valid for describing a hysteretic behavior. In this way the characterization of …