Search results for "bifurcations"
showing 3 items of 13 documents
Intermittency in the homopolar disk-dynamo
2006
We study a modified Bullard dynamo and show that this system is equivalent to a nonlinear oscillator subject to a multiplicative noise. The stability analysis of this oscillator is performed. Two bifurcations are identified, first towards an \lq\lq intermittent\rq\rq state where the absorbing (non-dynamo) state is no more stable but the most probable value of the amplitude of the oscillator is still zero and secondly towards a \lq\lq turbulent\rq\rq (dynamo) state where it is possible to define unambiguously a (non-zero) most probable value around which the amplitude of the oscillator fluctuates. The bifurcation diagram of this system exhibits three regions which are analytically characteri…
Hidden attractors in Chua circuit: mathematical theory meets physical experiments
2022
AbstractAfter the discovery in early 1960s by E. Lorenz and Y. Ueda of the first example of a chaotic attractor in numerical simulation of a real physical process, a new scientific direction of analysis of chaotic behavior in dynamical systems arose. Despite the key role of this first discovery, later on a number of works have appeared supposing that chaotic attractors of the considered dynamical models are rather artificial, computer-induced objects, i.e., they are generated not due to the physical nature of the process, but only by errors arising from the application of approximate numerical methods and finite-precision computations. Further justification for the possibility of a real exi…
Data from: Theoretical conditions for the coexistence of viral strains with differences in phenotypic traits: a bifurcation analysis
2018
We investigate the dynamics of a wild-type viral strain which generates mutant strains differing in phenotypic properties for infectivity, virulence, and mutation rates. We study, by means of a mathematical model and bifurcation analysis, conditions under which the wild-type and mutant viruses, which compete for the same host cells, can coexist. The coexistence conditions are formulated in terms of the basic reproductive numbers of the strains, a maximum value of the mutation rate, and the virulence of the pathogens. The analysis reveals that parameter space can be divided into five regions, each with distinct dynamics, that are organised around degenerate Bogdanov-Takens and zero-Hopf bifu…