Analysis of a genetic-metabolic oscillator with piecewise linear models

Bifurcation analysis of a piecewise-linear impact oscillator with drift

We investigate the complex bifurcation scenarios occurring in the dynamic response of a piecewise-linear impact oscillator with drift, which is able to describe qualitatively the behaviour of impact drilling systems. This system has been extensively studied by numerical and analytical methods in the past, but its intricate bifurcation structure has largely remained unknown. For the bifurcation ...

An algebraically computable piecewise linear planar oscillator

A piecewise linear oscillator whose oscillation can be completely characterized by algebraic methods is studied. It represents up to the best of authors’s knowledge, the first example where all the oscillation properties can be determined for all the values of the bifurcation parameter, being not a perturbation of the harmonic oscillator. In fact, algebraic expressions for coordinates of repres...

Structural Identification of Piecewise-Linear Models of Genetic Regulatory Networks

We present a method for the structural identification of genetic regulatory networks (GRNs), based on the use of a class of Piecewise-Linear (PL) models. These models consist of a set of decoupled linear models describing the different modes of operation of the GRN and discrete switches between the modes accounting for the nonlinear character of gene regulation. They thus form a compromise betw...

Piecewise-linear models of genetic regulatory networks: theory and example

The experimental study of genetic regulatory networks has made tremendous progress in recent years resulting in a huge amount of data on the molecular interactions in model organisms. It is therefore not possible anymore to intuitively understand how the genes and interactions together influence the behavior of the system. In order to answer such questions, a rigorous modeling and analysis appr...

Qualitative Simulation of Genetic Regulatory Networks Using Piecewise-Linear Models