This paper aims to investigate Gaussian colored-noise-induced stochastic bifurcations and the dynamical influence of correlation time noise intensity in a bistable Duffing--Van der Pol oscillator. By using averaging method, theoretically, one can obtain stationary probability density function amplitude for oscillator reveal interesting dynamics under colored noise. Stochastic are discussed through qualitative change distribution, which indicates that system parameters, intensity, time,...

The probability density function of stochastic differential equations is governed by the Fokker-Planck (FP) equation. A novel machine learning method developed to solve general FP based on deep neural networks. proposed algorithm does not require any interpolation and coordinate transformation, which different from traditional numercial methods. main novelty this paper that penalty factors are introduced overcome local optimization for approach, corresponding setting rules given. Meanwhile,...

During the past few decades, several significant progresses have been made in exploring complex nonlinear dynamics and vibration suppression of conceptual aeroelastic airfoil models. Additionally, some new challenges arisen. To best author's knowledge, most studies are concerned with deterministic case; however, effects stochasticity encountered practical flight environments on dynamical behaviors systems neglected. Crucially, coupling interaction structure nonlinearities uncertainty...

Weak fault signals are often overwhelmed by strong noise or interference. The key issue in diagnosis is to accurately extract useful characteristics. Stochastic resonance an important signal processing method that utilizes enhance weak signals. In this paper, address the issues of output saturation and imperfect optimization potential structure models classical bistable stochastic (CBSR), we propose a piecewise asymmetric system. A two-state model used theoretically derive signal-to-noise...

Abstract A bistable toggle switch is a paradigmatic model in the field of biology. The dynamics system induced by Gaussian noise has been intensively investigated, but cannot incorporate large bursts typically occurring real experiments. This paper aims to examine effects variations from one protein imposed non-Gaussian Lévy noise, which able describe even jumps, on coherent and on/off via steady-state probability density, joint density mean first passage time. We find that burst due noises...

Gene transcriptional regulatory is an inherently noisy process. In this paper, the study of fluctuations in a gene system extended to case L\'evy noise, kind non-Gaussian noises which can describe unpredictable jump changes random environment. The stationary probability density given explore key roles noise networks. results demonstrate that parameters including intensity, stability index and skewness parameter induce switches between distinct gene-expression states. A further concern...

In this paper, we are concerned with the stochastic averaging principle for differential equations (SDEs) non-Lipschitz coefficients driven by fractional Brownian motion (fBm) of Hurst parameter [Formula: see text]. We define integrals respect to fBm in integral formulation SDEs as pathwise and adopt condition proposed Taniguchi (1992) which is a much weaker wider range applications. The averaged established. then use their corresponding solutions approximate original both sense mean square...

Rough energy landscape and noisy environment are two common features in many subjects, such as protein folding. Due to the wide findings of bursting or spiking phenomenon biology science, small diffusions mixing large jumps adopted model that can be properly described by Lévy noise. We combine noise with rough landscape, modeled a potential function superimposed fast oscillating function, study transport particle triple-well excited noise, rather than only perturbations. The probabilities...

As the fluctuations of internal bioelectricity nervous system is various and complex, external electromagnetic radiation induced by magnet flux on membrane can be described non-Gaussian type distribution Lévy noise. Thus, electrical activities in an improved Hindmarsh-Rose model excited noise are investigated some interesting modes exhibited. The leads to mode transition spatial phase, such as from rest state firing state, spiking with more spikes, bursting state. Then time points versus...

We propose a method to find an approximate theoretical solution the mean first exit time (MFET) of one-dimensional bistable kinetic system subjected additive Poisson white noise, by extending earlier used solve stationary probability density function. Based on Dynkin formula and properties Markov processes, equation is obtained. It infinite-order partial differential that rather difficult theoretically. Hence, using non-Gaussian property noise truncate for time, analytical derived combining...

Scaled Brownian motions (SBMs) with power-law time-dependent diffusivity have been used to describe various types of anomalous diffusion yet Gaussian observed in granular gases kinetics, turbulent diffusion, and molecules mobility cells, name a few. However, some these systems may exhibit non-Gaussian behavior which can be described by SBM diffusing (DD-SBM). Here, we numerically investigate both free confined DD-SBM models characterized fixed or stochastic scaling exponent diffusivity. The...

Nonlinear dynamical systems with control parameters may not be well modeled by shallow neural networks. In this paper, the stable fixed-point solutions, periodic and chaotic solutions of parameter-dependent Lorenz system are learned simultaneously via a very deep network. The proposed learning model consists large number identical linear layers, which provide excellent nonlinear mapping capability. Residual connections applied to ease flow information training dataset is further utilized....

The reliability of a pitch-plunge hypersonic airfoil in random fluctuating flow with both cubic and freeplay nonlinearity is examined. Hopf bifurcation dynamic responses the are performed. To analyze reliability, effects stochasticity on behaviors model discussed detail. Several unwanted phenomena that result failure structure induced by fluctuations. Subsequently, defined analyzed according to first passage criteria. different parameters investigated. Furthermore, nonlinear energy sink...