Search results for " bifurcation"
showing 10 items of 68 documents
Modelling prey-predator interactions in Messina beachrock pools
2020
Abstract The Strait of Messina (Sicily, Italy) attracts the interest of marine ecologists for the presence of a large variety of habitat and mutually-interacting communities. Among them, beachrock formations, despite their wide geographic distribution, which also includes the Mediterranean area, have been poorly investigated from the biotic viewpoint. In this paper, the spatial and seasonal variability of benthic megafauna from the Messina microtidal beachrock is described. Combining in situ collected data (measurements of abiotic parameters and underwater visual census) with theoretical post-processing analyses (analysis of similarity percentages and cluster analysis), we deduced the possi…
Dynamical Features of the MAP Kinase Cascade
2017
The MAP kinase cascade is an important signal transduction system in molecular biology for which a lot of mathematical modelling has been done. This paper surveys what has been proved mathematically about the qualitative properties of solutions of the ordinary differential equations arising as models for this biological system. It focuses, in particular, on the issues of multistability and the existence of sustained oscillations. It also gives a concise introduction to the mathematical techniques used in this context, bifurcation theory and geometric singular perturbation theory, as they relate to these specific examples. In addition further directions are presented in which the application…
Sustained oscillations in the MAP kinase cascade.
2016
Abstract The MAP kinase cascade is a network of enzymatic reactions arranged in layers. In each layer occurs a multiple futile cycle of phosphorylations. The fully phosphorylated substrate then serves as an enzyme for the layer below. This paper focuses on the existence of parameters for which Hopf bifurcations occur and generate periodic orbits. Furthermore it is explained how geometric singular perturbation theory allows to generalize results from simple models to more complex ones.
Modelling temperature-dependent dynamics of single and mixed infections in a plant virus
2022
Multiple viral infection is an important issue in health and agriculture with strong impacts on society and the economy. Several investigations have dealt with the population dynamics of viruses with different dynamic properties, focusing on strain competition during multiple infections and the effects on viruses’ hosts. Recent interest has been on how multiple infections respond to abiotic factors such as temperature (T). This is especially important in the case of plant pathogens, whose dynamics could be affected significantly by global warming. However, few mathematical models incorporate the effect of T on parasite fitness, especially in mixed infections. Here, we investigate simple mat…
Almost Planar Homoclinic Loops in R3
1996
AbstractIn this paper we study homoclinic loops of vector fields in 3-dimensional space when the two principal eigenvalues are real of opposite sign, which we call almost planar. We are interested to have a theory for higher codimension bifurcations. Almost planar homoclinic loop bifurcations generically occur in two versions “non-twisted” and “twisted” loops. We consider high codimension homoclinic loop bifurcations under generic conditions. The generic condition forces the existence of a 2-dimensional topological invariant ring (non necessarily unique), which is a topological cylinder in the “non-twisted” case and a topological Möbius band in the “twisted” case. If the third eigenvalue is…
Observation of Poincaré-Andronov-Hopf Bifurcation in Cyclotron Maser Emission from a Magnetic Plasma Trap.
2018
We report the first experimental evidence of a controlled transition from the generation of periodic bursts of electromagnetic radiation into the continuous-wave regime of a cyclotron maser formed in magnetically confined nonequilibrium plasma. The kinetic cyclotron instability of the extraordinary wave of weakly inhomogeneous magnetized plasma is driven by the anisotropic electron population resulting from electron cyclotron plasma heating in a MHD-stable minimum-$B$ open magnetic trap.
Mechanistic Investigations of the BZ Reaction with Oxalic Acid Substrate. I. The Oscillatory Parameter Region and Rate Constants Measured for the Rea…
2004
This paper is the first part of a study reinvestigating the mechanism of the Belousov-Zhabotinsky (BZ) reaction of oxalic acid, which is the simplest organic substrate for a BZ oscillator. New experiments are performed to find the oscillatory region in 1 M sulfuric acid at 20 °C. The removal rate of the end product bromine by an inert gas stream is a critical parameter here: oscillations can be observed only in a window of that parameter. The “rate constant” for the physical removal of bromine is measured as a function of the gas flow rate and reactor volume; furthermore, the rate constants of three component reactions important in this system are also determined. These are oxygen atom tran…
Coexistence of single-mode and multi-longitudinal mode emission in the ring laser model
2005
A homogeneously broadened unidirectonal ring laser can emit in several longitudinal modes for large enough pump and cavity length because of Rabi splitting induced gain. This is the so called Risken-Nummedal-Graham-Haken (RNGH) instability. We investigate numerically the properties of the multi-mode solution. We show that this solution can coexist with the single-mode one, and its stability domain can extend to pump values smaller than the critical pump of the RNGH instability. Morevoer, we show that the multi-mode solution for large pump values is affected by two different instabilities: a pitchfork bifurcation, which preserves phase-locking, and a Hopf bifurcation, which destroys it.
Perturbations of symmetric elliptic Hamiltonians of degree four
2006
AbstractIn this paper four-parameter unfoldings Xλ of symmetric elliptic Hamiltonians of degree four are studied. We prove that in a compact region of the period annulus of X0 the displacement function of Xλ is sign equivalent to its principal part, which is given by a family induced by a Chebychev system; and we describe the bifurcation diagram of Xλ in a full neighborhood of the origin in the parameter space, where at most two limit cycles can exist for the corresponding systems.
Chreod.
2020
The concept of chreod was introduced in 1957 by the English theoretical biologist Conrad Hal Waddington (cf. Waddington: 1957; Galperin: 2008). From a linguistic point of view, the word “chreod” is a neologism, or, more precisely, a compound formed by the combination of two Greek words: the verb chre- (“it is necessary, must”) and the substantive -hodos (“way, road”). Therefore, it means literally “obliged pathway” (cf. Fabris 2018: 252, n. 6). Of course, such an etymology covers only a little bit of the semantic repertoire deployed by chreod. But, it is however true that some aspects of the biology of living systems can be described in these terms. Indeed, at the most general level, the id…