Narrow Results

In this paper, we investigate a single species model in a polluted closed environment with pulse toxicant input at fixed moment. We show that the population is extinct when the impulsive period is less than some critical value, otherwise the population is permanent, and the permanent condition also assure that there exists a unique positive periodic solution which is globally asymptotically stable. By comparing with the continuous system, we show that pulse toxicant input cause a periodic behavior in our system and oscillation of the solution. From the biological point of view, it is easy to protect species by changing impulsive period of the exogenous input of toxicant, and toxicant input amount, etc. Further, the effects of environmental noise on the population are studied by using numerical methods.

This paper is concerned with a two-dimensional stochastic Lotka–Volterra mutualistic parasite–host system with Lévy jumps. First, the study reveals that each species is either extinct or persistent in the mean, relying on some critical values. The result shows that both the environmental noises and Lévy jumps play important roles in determining the persistent in the mean or extinction of each species. Then, we establish the sufficient criteria for stability on distribution of the system. Finally, we give some numerical simulations to support the main results. Some recent works are extended and improved greatly.

In this paper, a deterministic size-dependent phytoplankton–zooplankton (PZ) model with additive Allee effect as well as its stochastic differential equation version is formulated to explore the growth dynamic of phytoplankton. A stability and Hopf bifurcation analysis is performed towards deterministic PZ model, and stochastic dynamic analysis is carried out on the stochastic PZ model, including the stochastic extinction, persistence in mean and the unique ergodic stationary distribution, which in turn provides a theoretical basis for numerical simulation analysis. Numerical simulations reveal that the synergistic effect of plankton body size and Allee effect can have a complex impact on the growth of phytoplankton in the deterministic and stochastic environments. One of the most interesting findings suggests that the reduced phytoplankton cell size can trigger bistable phenomenon, while the increased phytoplankton cell size or the weakened Allee effect has the ability to destroy such bistable phenomenon.

The need to analyze aircraft noise over ground with general properties occurs in various applications, most notably in environmental engineering, where the analysis of the sound pressure level (SPL) distribution near the ground due to aircraft noise is desired. Since the human hearing range is very wide, the determination of the SPL distribution for a given source spectrum is not trivial and may be regarded as a multiscale problem. One has to solve repeatedly, for many different wave numbers, the Helmholtz equation in the upper half space while imposing the given impedance boundary condition on the possibly non-flat ground. An efficient Helmholtz solver must therefore be incorporated in the scheme that finds the SPL distribution. Three totally different computational methods that may be used to solve this problem are considered here: A fictitious sources method, a parabolic approximation method and a wave-enriched finite element method (with two versions: PUM and GFEM). The three methods are compared in terms of their computational properties, and numerical examples are presented to demonstrate their performance.

Acoustic barriers are a well-known environmental noise mitigation solution, which is widely used nowadays. In this work, it is expected to contribute to the body of knowledge regarding the physical and technical behavior of those barriers by developing and implementing a set of models that allow an accurate analysis of noise barriers with new configuration types. A 2.5D boundary-only numerical model is developed and implemented, and computational analyses are performed in order to compare different surface profiles of the acoustic barriers. The particular case in which two acoustic barriers are used, one at each side of the road, is addressed.

The present paper investigates the influence of environmental noise on a fairly realistic three-species food chain model based on the Leslie-Gower scheme. The self- growth parameter for the prey species is assumed to be perturbed by white noise characterized by a Gaussian distribution with mean zero and unit spectral density. Using tools borrowed from the nonlinear dynamical system theory, we study the dynamical behavior of the model system. The behavior of the stochastic system (perturbed one) is studied and the fluctuations in the populations are measured both analytically (for the linearized system) and numerically by computer simulation. Varying one of the control parameters in its range, while keeping all the others constant, we monitor the changes in the dynamical behavior of the model system, thereby fixing the regimes in which the system exhibits chaotic dynamics. Our study suggests that the trophic level (top, middle or bottom) at which a population is positioned, the amplitude of environmental noise and the population's susceptibility to environmental noise play key roles in how noise affects the population dynamics.

A plenum window with incorporation of rectangular sonic crystals (SCs) in between two glass panes was tested in a reverberation room. Before the start of the experiment, numerical studies were performed on the whole structure in order to prove the effectiveness of the SCs in enhancing the noise attenuation performance of the plenum window. The effects of flat and jagged flaps on reducing strength of diffracted sound were also investigated in the experimental studies. White, traffic and construction noises were examined during each measurement. When the frequencies were ranging from 100Hz to 5000Hz, the plenum window with SCs without flap was able to attenuate 9.5, 8.5 and 8.6dBA of white, traffic and construction noises, respectively, compared with the case of without window. The effects of flat flaps on noise attenuation performance of the plenum window were negligible while the jagged flap was able to attenuate additional 1.7dBA of white noise and 1.6dBA of traffic and construction noises compared with the case of without flap. In the narrow frequency range of 900–1300Hz, the plenum window with SCs without flap was able to reduce additional 2.7, 2.3 and 2.5dBA of white, traffic and construction noises, respectively, compared with the case of without SCs.

We analyze the dynamics of both entanglement and quantum discord (QD) in a system of two non-interacting flux-qubits initially prepared in a Bell's state and subjected to either static or random telegraph noises (RTNs). Both independent and common sources of system-environment coupling are considered either in the Markovian or non-Markovian regime and the results are compared to those of ordinary qubits. Under suitable conditions, both entanglement and QD are more robust in flux-qubit systems than classical ones. In the Markovian regime where the decay is monotonic, they are both stronger in different environment coupling than in common coupling, while the opposite is found in the non-Markovian regime where the dynamics is stressed by sudden death and revival phenomena, more robust in qubits than in flux-qubits under dynamical RTN. Weakness of revival amplitudes is interpreted as a noise spectrum-related induced interaction affecting quantum features of the system, while energy level non-degeneracy (at zero-splitting) of flux-qubits induces a phase factor that set conditions under which entangled states can be experimentally witnessed in flux-qubit systems. Note that the energy levels non-degeneracy has no particular effect on other entanglement measures apart from entanglement witnesses.

We investigate the dynamics of entanglement, quantum discord (QD) and state coherence in a bipartite and noninteracting spin-qutrits system under mixed classical noises. Specifically, the collective effects of static noise (SN) and random telegraphic noise (RTN) each being coupled with a marginal system, are analyzed. While the static noise models a non-Markovian environment, the dynamic noise can model both a Markovian or a non-Markovian environment, and both dynamics are studied. We show that quantum correlations and coherence may survive the noise degrading effects at sufficiently long time when the Markovian regime of the RTN is considered. Meanwhile, the opposite is found in the non-Markovian regime, wherein the nonmonotonic dynamics of quantum features avoid sudden death phenomena. However, the static noise is more fatal to the survival of quantum correlations and quantum state coherence as compared to the RTN.