Hopf bifurcations in coronal loops. I - Stability conditions for static equilibrium. II - Nonlinear evolution of instabilities

The current theoretical understanding of the linear and nonlinear evolution of resistive tearing instabilities in sheared magnetic fields is reviewed. The physical mechanisms underlying this instability are emphasized. Some of the problems which are encountered in developing a model of magnetic energy dissipation in coronal loops are discussed and possible solutions are suggested.

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Identifying stability conditions and Hopf bifurcations in a consumer resource model using a consumption threshold

Ecological Complexity ◽

10.1016/j.ecocom.2016.03.002 ◽

2016 ◽

Vol 28 ◽

pp. 212-217 ◽

Cited By ~ 2

Author(s):

K.J. Duffy ◽

O.C. Collins

Keyword(s):

Hopf Bifurcations ◽

Stability Conditions ◽

Resource Model ◽

Consumer Resource

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DYNAMICS IN AN SIR MODEL WHEN VACCINATION DEMAND FOLLOWS PRIOR LEVELS OF DISEASE PREVALENCE

Advances in Complex Systems ◽

10.1142/s0219525915500216 ◽

2015 ◽

Vol 18 (07n08) ◽

pp. 1550021 ◽

Cited By ~ 1

Author(s):

JOHN C. ECKALBAR ◽

PETE TSOURNOS ◽

WALTER L. ECKALBAR

Keyword(s):

Sir Model ◽

Disease Prevalence ◽

Childhood Vaccination ◽

Hopf Bifurcations ◽

Stability Conditions ◽

Policy Interventions ◽

Parameter Values ◽

Disease Free

This paper investigates an susceptible, infectious, recovered (SIR) model with childhood vaccination demand modeled as a function of prior levels of disease prevalence. Stability conditions for endemic and disease-free equilibria are uncovered, and both Hopf bifurcations and chaos are found with certain constellations of parameter values. Policy interventions directed toward increasing vaccination are explored, and the implied magnitudes of the external benefit of vaccination are modeled.

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INDETERMINACY, BIFURCATIONS, AND UNEMPLOYMENT FLUCTUATIONS

Macroeconomic Dynamics ◽

10.1017/s1365100508070211 ◽

2008 ◽

Vol 12 (S1) ◽

pp. 75-89 ◽

Cited By ~ 10

Author(s):

FRÉDÉRIC DUFOURT ◽

TERESA LLOYD-BRAGA ◽

LEONOR MODESTO

Keyword(s):

Steady State ◽

Returns To Scale ◽

Elasticity Of Substitution ◽

Hopf Bifurcations ◽

Stability Conditions ◽

Simple Extension ◽

Unemployment Benefits ◽

Local Dynamics ◽

Labor Taxation ◽

Constant Returns To Scale

We incorporate imperfectly insured unemployment in the finance constrained economy proposed by Woodford (1986), by introducing unions and unemployment benefits financed by labor taxation. We show that this simple extension of the Woodford model changes drastically its stability conditions and local dynamics around the steady state. In fact, in contrast to related models in the literature, we find that, under constant returns to scale in production: (i) indeterminacy always prevails in the case of a unitary elasticity of substitution between capital and labor and (ii) flip and Hopf bifurcations occur for empirically credible elasticities of substitution between capital and labor, so that a rich set of dynamics may emerge at “realistic” parameters' values.

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Siphon Flows in Stratified Coronal Loops

International Astronomical Union Colloquium ◽

10.1017/s0252921100025288 ◽

1994 ◽

Vol 144 ◽

pp. 185-187

Author(s):

S. Orlando ◽

G. Peres ◽

S. Serio

Keyword(s):

Heat Flux ◽

Scaling Laws ◽

Flow Model ◽

Supersonic Flows ◽

Coronal Loops ◽

Characteristic Parameters

AbstractWe have developed a detailed siphon flow model for coronal loops. We find scaling laws relating the characteristic parameters of the loop, explore systematically the space of solutions and show that supersonic flows are impossible for realistic values of heat flux at the base of the upflowing leg.

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