Search results for "bifurcation"
showing 10 items of 204 documents
On asymmetric periodic solutions in relay feedback systems
2021
Abstract Asymmetric self-excited periodic motions or periodic solutions which are produced by relay feedback systems that have symmetric characteristics are studied in the paper. Two different mechanisms of producing an asymmetric oscillation by a system with symmetric properties are noted and analyzed by the locus of a perturbed relay system (LPRS) method. Bifurcation between the ability to excite symmetric and asymmetric oscillation with variation of system parameters is analyzed. An algorithm of finding asymmetric solutions is proposed.
Stability analysis of a paramagnetic spheroid in a precessing field
2019
Abstract The stability of a paramagnetic prolate or oblate spheroidal particle in a precessing magnetic field is studied. The bifurcation diagram is calculated analytically as a function of the magnetic field frequency and the precession angle. The orientation of the particle in the synchronous regime is calculated. The rotational dynamics and the mean rotational frequency in the asynchronous regime are also obtained. The theoretical model we describe enables the analytic calculation of the dynamics of the particle in the limiting case when the motion is periodic. The theoretical models were also compared with experimental results of rod like particle dynamics in a precessing magnetic field…
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…
Dynamic complexities in host-parasitoid interaction
1999
In the 1970s ecological research detected chaos and other forms of complex dynamics in simple population dynamics models, initiating a new research tradition in ecology. However, the investigations of complex population dynamics have mainly concentrated on single populations and not on higher dimensional ecological systems. Here we report a detailed study of the complicated dynamics occurring in a basic discrete-time model of host-parasitoid interaction. The complexities include (a) non-unique dynamics, meaning that several attractors coexist, (b) basins of attraction (defined as the set of the initial conditions leading to a certain type of an attractor) with fractal properties (pattern of…
Non-unique population dynamics: basic patterns
2000
We review the basic patterns of complex non-uniqueness in simple discrete-time population dynamics models. We begin by studying a population dynamics model of a single species with a two-stage, two-habitat life cycle. We then explore in greater detail two ecological models describing host‐macroparasite and host‐parasitoid interspecific interactions. In general, several types of attractors, e.g. point equilibria vs. chaotic, periodic vs. quasiperiodic and quasiperiodic vs. chaotic attractors, may coexist in the same mapping. This non-uniqueness also indicates that the bifurcation diagrams, or the routes to chaos, depend on initial conditions and are therefore non-unique. The basins of attrac…
Transition to turbulence in serpentine pipes
2017
Abstract The geometry considered in the present work (serpentine pipe) is a sequence of U-bends of alternate curvature. It is characterized by pipe diameter, d = 2a and bend diameter, D = 2c. The repeated curvature inversion forces the secondary flow pattern, typical of all flows in curved ducts, to switch between two mirror-like configurations. This causes (i) pressure drop and heat or mass transfer characteristics much different from those occurring either in a straight pipe or in a constant-curvature pipe, and (ii) an early loss of stability of the base steady-state flow. In the present work, four values of the curvature δ = a/c (0.2, 0.3, 0.4 and 0.5) were considered. For each value of …
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…
Viral replication modes in single-peak fitness landscapes: A dynamical systems analysis
2017
Positive-sense, single-stranded RNA viruses are important pathogens infecting almost all types of organisms. Experimental evidence from distributions of mutations and from viral RNA amplification suggest that these pathogens may follow different RNA replication modes, ranging from the stamping machine replication (SMR) to the geometric replication (GR) mode. Although previous theoretical work has focused on the evolutionary dynamics of RNA viruses amplifying their genomes with different strategies, little is known in terms of the bifurcations and transitions involving the so-called error threshold (mutation-induced dominance of mutants) and lethal mutagenesis (extinction of all sequences du…
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.
Stability of stationary solutions in models of the Calvin cycle
2017
Abstract In this paper results are obtained concerning the number of positive stationary solutions in simple models of the Calvin cycle of photosynthesis and the stability of these solutions. It is proved that there are open sets of parameters in the model of Zhu et al. (2009) for which there exist two positive stationary solutions. There are never more than two isolated positive stationary solutions but under certain explicit special conditions on the parameters there is a whole continuum of positive stationary solutions. It is also shown that in the set of parameter values for which two isolated positive stationary solutions exist there is an open subset where one of the solutions is asym…