333 research outputs found
Weakly coupled two slow- two fast systems, folded node and mixed mode oscillationsM
We study Mixed Mode Oscillations (MMOs) in systems of two weakly coupled
slow/fast oscillators. We focus on the existence and properties of a folded
singularity called FSN II that allows the emergence of MMOs in the presence of
a suitable global return mechanism. As FSN II corresponds to a transcritical
bifurcation for a desingularized reduced system, we prove that, under certain
non-degeneracy conditions, such a transcritical bifurcation exists. We then
apply this result to the case of two coupled systems of FitzHugh- Nagumo type.
This leads to a non trivial condition on the coupling that enables the
existence of MMOs
Emergence of Cooperation in Non-scale-free Networks
Evolutionary game theory is one of the key paradigms behind many scientific
disciplines from science to engineering. Previous studies proposed a strategy
updating mechanism, which successfully demonstrated that the scale-free network
can provide a framework for the emergence of cooperation. Instead, individuals
in random graphs and small-world networks do not favor cooperation under this
updating rule. However, a recent empirical result shows the heterogeneous
networks do not promote cooperation when humans play a Prisoner's Dilemma. In
this paper, we propose a strategy updating rule with payoff memory. We observe
that the random graphs and small-world networks can provide even better
frameworks for cooperation than the scale-free networks in this scenario. Our
observations suggest that the degree heterogeneity may be neither a sufficient
condition nor a necessary condition for the widespread cooperation in complex
networks. Also, the topological structures are not sufficed to determine the
level of cooperation in complex networks.Comment: 6 pages, 5 figure
Fence-sitters Protect Cooperation in Complex Networks
Evolutionary game theory is one of the key paradigms behind many scientific
disciplines from science to engineering. In complex networks, because of the
difficulty of formulating the replicator dynamics, most of previous studies are
confined to a numerical level. In this paper, we introduce a vectorial
formulation to derive three classes of individuals' payoff analytically. The
three classes are pure cooperators, pure defectors, and fence-sitters. Here,
fence-sitters are the individuals who change their strategies at least once in
the strategy evolutionary process. As a general approach, our vectorial
formalization can be applied to all the two-strategies games. To clarify the
function of the fence-sitters, we define a parameter, payoff memory, as the
number of rounds that the individuals' payoffs are aggregated. We observe that
the payoff memory can control the fence-sitters' effects and the level of
cooperation efficiently. Our results indicate that the fence-sitters' role is
nontrivial in the complex topologies, which protects cooperation in an indirect
way. Our results may provide a better understanding of the composition of
cooperators in a circumstance where the temptation to defect is larger.Comment: an article with 6 pages, 3 figure
On a coupled time-dependent SIR models fitting with New York and New-Jersey states COVID-19 data
This article describes a simple Susceptible Infected Recovered (SIR) model
fitting with COVID-19 data for the month of march 2020 in New York (NY) state.
The model is a classical SIR, but is non-autonomous; the rate of susceptible
people becoming infected is adjusted over time in order to fit the available
data. The death rate is also secondarily adjusted. Our fitting is made under
the assumption that due to limiting number of tests, a large part of the
infected population has not been tested positive. In the last part, we extend
the model to take into account the daily fluxes between New Jersey (NJ) and NY
states and fit the data for both states. Our simple model fits the available
data, and illustrates typical dynamics of the disease: exponential increase,
apex and decrease. The model highlights a decrease in the transmission rate
over the period which gives a quantitative illustration about how lockdown
policies reduce the spread of the pandemic. The coupled model with NY and NJ
states shows a wave in NJ following the NY wave, illustrating the mechanism of
spread from one attractive hot spot to its neighbor.
A method to discriminate between localized and chaotic quantum systems
We derive a criterion that distinguishes whether a generic isolated quantum
system initially set out of equilibrium can be considered as localized close to
its initial state, or chaotic. Our approach considers the time evolution in the
Lanczos basis, which maps the system's dynamics onto that of a particle moving
in a one-dimensional lattice where both the energy in the lattice sites and the
tunneling from one lattice site to the next are inhomogeneous. We infer a
criterion that allows distinguishing localized from chaotic systems. This
criterion involves the coupling strengths between Lanczos states and their
expectation energy fluctuations. We verify its validity by inspecting three
cases, corresponding to Anderson localization as a function of dimension, the
out-of-equilibrium dynamics of a many-body dipolar spin system, and integrable
systems. We finally show that our approach provides a justification for the
Wigner surmise and the eigenstate thermalization hypothesis, which have both
been proposed to characterize quantum chaotic systems. Indeed, our criterion
for a system to be chaotic implies the level repulsion (also known as spectral
rigidity) of eigenenergies, which is characteristic of the Wigner-Dyson
distribution; and we also demonstrate that in the chaotic regime, the
expectation value of any local observable only weakly varies as a function of
eigenstates. Our demonstration allows to define the class of operators to which
the eigenstate thermalization applies, as the ones that connect states that are
coupled at weak order by the Hamiltonian.Comment: 15 pages, 6 figure
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