scholarly journals Perturbation of a Hopf bifurcation by an external time-periodic forcing

1985 ◽  
Vol 57 (2) ◽  
pp. 172-199 ◽  
Author(s):  
J.M Gambaudo
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Forcing ◽  
External Time ◽  
Time Periodic

Temporal Forcing Induced Pattern Transitions Near the Turing–Hopf Bifurcation in a Plankton System

2020 ◽  
Vol 30 (09) ◽  
pp. 2050136
Author(s):  
Wen Wang ◽  
Shutang Liu ◽  
Zhibin Liu ◽  
Da Wang
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Oscillation ◽  
Reaction Diffusion ◽  
Periodic Forcing ◽  
Diffusion Type ◽  
Weakly Nonlinear ◽  
Form Analysis ◽  
The Impact ◽  
Time Periodic ◽  
Theoretical Results

We explore the impact of time-periodic forcing on pattern transitions in a plankton system of reaction–diffusion type. Here, we mainly focus on the forced states near the Turing–Hopf bifurcation. A normal form analysis leads to the finding that weak forcing exhibits a destabilizing effect on the dynamics by exciting the transitions from a spatially homogeneous stationary state to a periodic oscillation in time. The results are obtained by studying the amplitude equations derived using weakly nonlinear analysis in the presence of forcing, which enables us to calculate the changes of states. Examples are given to confirm the theoretical results.

Electromagnetic Induction in a Stratified Conducting Half-Space by an Arbitrary Periodic Source

1973 ◽  
Vol 51 (10) ◽  
pp. 1064-1074 ◽  
Author(s):  
D. M. Summers ◽  
J. T. Weaver
Keyword(s):  
Half Space ◽  
Recursion Formula ◽  
Electric And Magnetic Fields ◽  
Hertz Potential ◽  
Infinite Line ◽  
The Fourier Transform ◽  
The One ◽  
External Time ◽  
Entire Theory ◽  
Time Periodic

A general theory of induction in a horizontally stratified plane conductor by an external, time-periodic, magnetic source is presented. The analysis is a generalization to the case of an N-layered conductor of a previously published theory for induction in a uniform conducting half-space, in which the electromagnetic field was expressed in terms of electric and magnetic Hertz vectors oriented normally to the surface of the conductor. With the aid of this representation the entire theory is developed in terms of the one scalar component of the magnetic Hertz vector. Solutions for the electric and magnetic fields above and within the conductor are obtained in the form of double integrals whose integrands are related through a recursion formula to the Fourier transform of the magnetic Hertz potential of the source evaluated at the surface of the conductor. Special formulas applicable to 1- and 2-layer conductors are derived and the form of solution for some elementary sources is also discussed. As an illustration of the theory, numerical calculations are given for an infinite line current above a 10-layer conductor whose conductivity increases (i) linearly and (ii) exponentially with depth.

Time-periodic spatially periodic planforms in Euclidean equivariant partial differential equations

1995 ◽  
Vol 352 (1698) ◽  
pp. 125-168 ◽  
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Pattern ◽  
Invariant Equilibrium ◽  
Periodic Patterns ◽  
Planar Lattice ◽  
Diffusive Convection ◽  
Spatially Periodic ◽  
Spatio Temporal ◽  
Boussinesq Fluid ◽  
Time Periodic

In Rayleigh-Bénard convection, the spatially uniform motionless state of a fluid loses stability as the Rayleigh number is increased beyond a critical value. In the simplest case of convection in a pure Boussinesq fluid, the instability is a symmetry-breaking steady-state bifurcation that leads to the formation of spatially periodic patterns. However, in many double-diffusive convection systems the heat-conduction solution actually loses stability via Hopf bifurcation. These hydrodynamic systems provide motivation for the present study of spatiotemporally periodic pattern formation in Euclidean equivariant systems. We call such patterns planforms . We classify, according to spatio-temporal symmetries and spatial periodicity, many of the time-periodic solutions that may be obtained through equivariant Hopf bifurcation from a group-invariant equilibrium. Instead of focusing on plan- forms periodic with respect to a specified planar lattice, as has been done in previous investigations, we consider all planforms that are spatially periodic with respect to some planar lattice. Our classification results rely only on the existence of Hopf bifurcation and planar Euclidean symmetry and not on the particular dif­ferential equation.

Active Control Methods for Drag Reduction in Flow Over Bluff Bodies (Keynote)

2002 ◽  
Author(s):  
Haecheon Choi
Keyword(s):  
Circular Cylinder ◽  
Drag Reduction ◽  
Active Control ◽  
High Frequency ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Control Methods ◽  
Periodic Forcing ◽  
Time Periodic

In this paper, we present two successful results from active controls of flows over a circular cylinder and a sphere for drag reduction. The Reynolds number range considered for the flow over a circular cylinder is 40∼3900 based on the free-stream velocity and cylinder diameter, whereas for the flow over a sphere it is 105 based on the free-stream velocity and sphere diameter. The successful active control methods are a distributed (spatially periodic) forcing and a high-frequency (time periodic) forcing. With these control methods, the mean drag and lift fluctuations decrease and vortical structures are significantly modified. For example, the time-periodic forcing with a high frequency (larger than 20 times the vortex shedding frequency) produces 50% drag reduction for the flow over a sphere at Re = 105. The distributed forcing applied to the flow over a circular cylinder results in a significant drag reduction at all the Reynolds numbers investigated.

Induction of floquet topological phases in honeycomb nanoribbon irradiated by circularly polarized laser field

2021 ◽  
pp. 2150180
Author(s):  
Chol Jun Kang ◽  
Mun Gwon Jo
Keyword(s):  
Energy Spectrum ◽  
Laser Field ◽  
Low Frequency ◽  
Edge States ◽  
Circularly Polarized ◽  
Properties Of Materials ◽  
The Stability ◽  
External Time ◽  
Time Periodic ◽  
Topological Phase Transitions

The stability of the existence of the topological properties even in non-equilibrium condition such as irradiation of external time-periodic perturbation paves the way for designing and controlling the properties of materials. We study the change in the structure of the quasi-energy spectrum under the influence of the circularly polarized laser field with various intensities. The system is two-dimensional honeycomb nanoribbon of having zig-zag edges. Two cases where the onsite energies are present and absent are considered. We find that the topological phase transitions occur at some critical intensities of the laser field in both cases, which are recognized by the gap closing, the appearance of two crossing edge states, and sudden raise of the first Chern number from 0 to 1. The critical laser intensity is raised when either the frequency increases or the width of the ribbon decreases. Furthermore, band folding is observed in low-frequency domain in the quasi-energy spectrum and becomes more pronounced for the lower frequencies.

The paradox of enrichment, spatial heterogeneity, community effects and the phenomenon of apparent disappearance in the marine bacteriophage dynamics

2021 ◽  
Vol 62 ◽  
pp. 453-468
Author(s):  
Andrei Korobeinikov ◽  
Elena Shchepakina ◽  
Vladimir Sobolev Sobolev
Keyword(s):  
Mathematical Model ◽  
Hopf Bifurcation ◽  
External Factors ◽  
Loss Of Stability ◽  
Simple Mathematical Model ◽  
Community Effects ◽  
Periodic Forcing ◽  
Internal Factors ◽  
High Magnitude ◽  
Microbial Systems

In aquatic microbial systems, high magnitude variations in abundance, such as sudden blooms alternating with comparatively long periods of very low abundance ("apparent disappearance'') are relatively common. The authors suggest that, in order to occur, such variations in abundance in microbial systems and, in particular, the apparent disappearance of species do not require seasonal or periodic forcing of any kind, or external factors of any other nature, and can be caused by internal factors, and in particular by bacteria-phage interaction. Specifically, the authors suggest that the variations in abundance and the apparent disappearance phenomenon can be a result of phage infection and the lysis of infected bacteria. To illustrate this idea, the authors consider a reasonably simple mathematical model of bacteria-phage interaction based on the model suggested by Edoardo Beretta and Yang Kuang, which assumes neither periodic forcing, nor action of other external factors. The model admits a loss of stability via Andronov-Hopf bifurcation and exhibits dynamics which is able to explains the phenomenon. These properties of the model are especially distinctive for spatially non-homogeneous biosystems as well as biosystem with some sorts of cooperation or community effects. doi:10.1017/S1446181120000085

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