How copper contamination pulses shape the regimeshifts of phytoplankton−zooplankton dynamics?

In this study, we consider the effects of impulsive copper contaminationof the phytoplankton−zooplankton dynamics. We use the model on interactionsbetween algae and Daphnia with deterministic and stochastic impulsecopper contamination. In low environmental copper concentration(Cucst 28μgL−1) minimal of copper concentrations. In intermediateconcentrations, deterministic and stochastic pulses may transformpopulation dynamics in complex oscillations. Bifurcation diagram was computedto illustrate the different type observed dynamics in an environmentwith pulses of contamination. Depending on minimum copper concentrationin the environment, this bifurcation diagram highlighted, the resilience orthe regime shifts of the system in occurrence of pulse contamination. Ourstudy may contribute to the prevalence of underestimation of extinction riskor population regime shifts from random fluctuations of pollution in rea

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

Global stability analysis of birhythmicity in a self-sustained oscillator

We analyze global stability properties of birhythmicity in a self-sustained system with random excitations. The model is a multi-limit cycles variation of the van der Pol oscillatorintroduced to analyze enzymatic substrate reactions in brain waves. We show that the two frequencies are strongly influenced by the nonlinear coefficients $\alpha$ and $\beta$. With a random excitation, such as a Gaussian white noise, the attractor's global stability is measured by the mean escape time $\tau$ from one limit-cycle. An effective activation energy barrier is obtained by the slope of the linear part of the variation of the escape time $\tau$ versus the inverse noise-intensity 1/D. We find that the trapping barriers of the two frequencies can be very different, thus leaving the system on the same attractor for an overwhelming time. However, we also find that the system is nearly symmetric in a narrow range of the parameters.Comment: 17 pages, 8 figures, to appear on Choas, 201

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.

Stability of synchronization in a shift-invariant ring of mutually coupled oscillators

This paper treats synchronization dynamics in a shift-invariant ring of N mutually coupled self-sustained electrical units. Via some qualitative theory for the Lyapunov exponents, we derive the regimes of coupling parameters for which synchronized oscillation is stable or unstable in the ring