7 research outputs found
Symmetry breaking in driven and strongly damped pendulum
We examine the conditions for appearance of symmetry breaking bifurcation in
damped and periodically driven pendulum in the case of strong damping. We show
that symmetry breaking, unlike other nonlinear phenomena, can exist at high
dissipation. We prove that symmetry breaking phases exist between phases of
symmetric normal and symmetric inverted oscillations. We find that symmetry
broken solutions occupy a sufficiently smaller region of pendulum's parameter
space in comparison to the statements made in earlier considerations [McDonald
and Plischke, Phys. Rev. B 27 (1983) 201]. Our research on symmetry breaking in
a strongly damped pendulum is relevant to an understanding of phenomena of
dynamic symmetry breaking and rectification in a pure ac driven semiconductor
superlattices.Comment: 11 pages, 4 color figures, RevTeX
Stability properties of periodically driven overdamped pendula and their implications to physics of semiconductor superlattices and Josephson junctions
We consider the first order differential equation with a sinusoidal
nonlinearity and periodic time dependence, that is, the periodically driven
overdamped pendulum. The problem is studied in the case that the explicit
time-dependence has symmetries common to pure ac-driven systems. The only
bifurcation that exists in the system is a degenerate pitchfork bifurcation,
which describes an exchange of stability between two symmetric nonlinear modes.
Using a type of Prufer transform to a pair of linear differential equations, we
derive an approximate condition of the bifurcation. This approximation is in
very good agreement with our numerical data. In particular, it works well in
the limit of large drive amplitudes and low external frequencies. We
demonstrate the usefulness of the theory applying it to the models of pure
ac-driven semiconductor superlattices and Josephson junctions. We show how the
knowledge of bifurcations in the overdamped pendulum model can be utilized to
describe effects of rectification and amplification of electric fields in these
microstructures.Comment: 15 pages, 7 figures, Revtex 4.1. Revised and expanded following
referee's report. Submitted to journal Chaos
Recommended from our members
The Net Worth Trap: Investment and Output Dynamics in the Presence of Financing Constraints
This paper investigates investment and output dynamics in a simple continuous time setting, showing that financing constraints substantially alter the relationship between net worth and the decisions of an optimizing firm. In the absence of financing constraints, net worth is irrelevant (the 1958 ModiglianiâMiller irrelevance proposition applies). When incorporating financing constraints, a decline in net worth leads to the firm reducing investment and also output (when this reduces risk exposure). This negative relationship between net worth and investment has already been examined in the literature. The contribution here is providing new intuitive insights: (i) showing how large and long lasting the resulting non-linearity of firm behaviour can be, even with linear production and preferences; and (ii) highlighting the economic mechanisms involvedâthe emergence of shadow prices creating both corporate prudential saving and induced risk aversion. The emergence of such pronounced non-linearity, even with linear production and preference functions, suggests that financing constraints can have a major impact on investment and output; and this should be allowed for in empirical modelling of economic and financial crises (for example, the great depression of the 1930s, the global financial crisis of 2007â2008 and the crash following the Covid-19 pandemic of 2020)
The net worth trap: investment and output dynamics in the presence of financing constraints
This paper investigates investment and output dynamics in a simple continuous time
setting, showing that financing constraints substantially alter the relationship between net worth
and the decisions of an optimizing firm. In the absence of financing constraints, net worth is
irrelevant (the 1958 ModiglianiâMiller irrelevance proposition applies). When incorporating financing
constraints, a decline in net worth leads to the firm reducing investment and also output (when
this reduces risk exposure). This negative relationship between net worth and investment has
already been examined in the literature. The contribution here is providing new intuitive insights: (i)
showing how large and long lasting the resulting non-linearity of firm behaviour can be, even with
linear production and preferences; and (ii) highlighting the economic mechanisms involvedâthe
emergence of shadow prices creating both corporate prudential saving and induced risk aversion. The
emergence of such pronounced non-linearity, even with linear production and preference functions,
suggests that financing constraints can have a major impact on investment and output; and this
should be allowed for in empirical modelling of economic and financial crises (for example, the great
depression of the 193