111 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
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.
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
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
Analysis of a spatio-temporal advection-diffusion model for human behaviors during a catastrophic event
In this work, using the theory of first-order macroscopic crowd models, we
introduce a compartmental advection-diffusion model, describing the
spatio-temporal dynamics of a population in different human behaviors (alert,
panic and control) during a catastrophic event. For this model, we prove the
local existence, uniqueness and regularity of a solution, as well as the
positivity and --boundedness of this solution. Then, in order to study the
spatio-temporal behavioral dynamics of a population during a catastrophic
event, we present several numerical simulations for different evacuation
scenarios.Comment: I will correct and modify some facts and I will submit again the new
versio
Effective Fokker-Planck Equation for Birhythmic Modified van der Pol Oscillator
We present an explicit solution based on the phase-amplitude approximation of
the Fokker-Planck equation associated with the Langevin equation of the
birhythmic modified van der Pol system. The solution enables us to derive
probability distributions analytically as well as the activation energies
associated to switching between the coexisting different attractors that
characterize the birhythmic system. Comparing analytical and numerical results
we find good agreement when the frequencies of both attractors are equal, while
the predictions of the analytic estimates deteriorate when the two frequencies
depart. Under the effect of noise the two states that characterize the
birhythmic system can merge, inasmuch as the parameter plane of the birhythmic
solutions is found to shrink when the noise intensity increases. The solution
of the Fokker-Planck equation shows that in the birhythmic region, the two
attractors are characterized by very different probabilities of finding the
system in such a state. The probability becomes comparable only for a narrow
range of the control parameters, thus the two limit cycles have properties in
close analogy with the thermodynamic phases
Permanence and periodic solution for a modified Leslie-Gower type predator-prey model with diffusion and non constant coefficients
In this paper we study a predator-prey system, modeling the interaction of two species with diffusion and T-periodic environmental parameters. It is a Leslie-Gower type predator-prey model with Holling-type-II functional response. We establish some sufficient conditions for the ultimate boundedness of solutions and permanence of this system. By constructing an appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Numerical simulations are presented to illustrate the results
United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS VIBRATIONS ANALYSIS AND BIFURCATIONS IN THE SELF-SUSTAINED ELECTROMECHANICAL SYSTEM WITH MU
Abstract We consider in this paper the dynamics of the self-sustained electromechanical system with multiple functions, consisting of an electrical Rayleigh-Duffing oscillator, magnetically coupled with linear mechanical oscillators. The averaging and the balance harmonic method are used to find the amplitudes of the oscillatory states respectively in the autonomous and non-autonomous cases, and analyze the condition in which the quenching of self-sustained oscillations appears. The effects of the number of linear mechanical oscillators on the behavior of the model are discussed. Various bifurcation structures, the stability chart and the variation of the Lyapunov exponent are obtained, using numerical simulations of the equations of motion.
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