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

Dynamics and Synchronization of Electromechanical Devices with a Duffing Linearity

For the technological exploitation in non-linear electromechanical engineering, we consider in this thesis the dynamics and synchronization of electromechanical device with a Duffing non-linearity, which are widely encountered in various branches of electromechanical engineering. The main purpose of this work is the study of the behaviour of such devices using analytical and numerical simulations of the equations of motion. Our aim is to find how the non-linear phenomena such as hysteresis and multi-stability phenomena, sub-harmonic, super-harmonic oscillations, and chaos can be used to improve industrial tasks like cutting and drilling. The problem of synchronizing electromechanical devices is also of great interest as well as the situation where the non-linearity is due to the discontinuity of the industrial devices.Pour une exploitation technologique possible en ingénierie électromécanique, nous considérons dans cette thèse l'étude dynamique et la synchronisation des dispositifs électromécaniques non-linéaires décrits par le système couplé constitué de l'oscillateur électrique de Duffing couplé magnétiquement et paramètriquement aux oscillateurs mécaniques linéaires en série et en parallèle. L'intérêt porté sur ces dispositifs électromécaniques revêt un caractère technologique indéniable, dû à sa présence dans plusieurs branches de l'ingénierie électromécanique. Nous étudions le comportement de ces dispositifs à travers les études analytique et numérique, et montrons que les phénomènes non-linéaires tels que: les phénomènes de résonances, d'anti-résonances, d'hystérésis et de multi-stabilité, les oscillations sous et super harmoniques, et le chaos peuvent être utilisé pour améliorer les perfectionnements à des taches industrielles. Le problème de synchronisation des états régulier et chaotique de ces dispositifs est aussi d'un grand intérêt pour des applications en ingénierie électromécanique

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

Environmental stochastic effects on phytoplankton–zooplankton dynamics

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