Journal of Nonlinear Science最新文献

Understanding the process of extinction in natural populations is crucial for the preservation of ecosystem stability and biodiversity, both theoretically and practically. The risk of extinction in these populations is often influenced by environmental stochasticity, which has a significant impact on birth and mortality rates. In this study, we propose a tri-trophic food chain model that incorporates random disturbances in the environment, represented by a chemostat, which is an ideal mathematical model for simulating diverse ecosystems. In the absence of noise, the model exhibits two types of bistability, indicating that the stochastic system has two distinct paths to extinction: from a stationary state or from an oscillatory state. For each type, we determine the tipping value of environmental stochasticity that leads to the extinction of top predators by constructing confidence regions for the corresponding coexisting attractor. Furthermore, we observe a high skewness and heavy-tailed distribution of extinction times for intermediate and high levels of environmental stochasticity, consistent with empirical data. To analyze extinction times, we employ the Lévy distribution, a statistical model that describes power-law tail distributions. Our findings demonstrate that, for a fixed dilution rate, increasing environmental stochasticity reduces the average extinction time, thereby accelerating species extinction. Additionally, for a certain level of stochasticity, the average extinction time decreases with the magnitude of the dilution rate due to the heavy-tailed nature of the extinction time distribution.

Methods from controlled Lagrangians, double-bracket dissipation and interconnection and damping assignment–passivity-based control (IDA-PBC) are used to construct nonlinear feedback controls which (asymptotically) stabilize previously unstable equilibria of Lie–Poisson Hamiltonian systems. The results are applied to find an asymptotically stabilizing control for the rotor driven satellite, and a stabilizing control for Hall magnetohydrodynamic flow.

Abstract

In this study, multiple higher-order pole solutions of spinor Bose–Einstein condensates are explored by means of the inverse scattering transform, which are associated with different higher-order pole pairs of the transmission coefficient and give solutions to the spin-1 Gross–Pitaevskii equation. First, a direct scattering problem is introduced to map the initial data to the scattering data, which includes discrete spectrums, reflection coefficients, and a polynomial that replaces the normalized constants. In order to analyze symmetries and discrete spectra in the direct scattering problem, a generalized cross product is defined in four-dimensional vector Space. The inverse scattering problem is then characterized in terms of the (4times 4) matrix Riemann–Hilbert problem that is subject to the residual conditions of these higher-order poles. In the reflectionless case, the Riemann–Hilbert problem can be converted into a linear algebraic system, which has a unique solution and allows us to explicitly obtain multiple higher-order pole solutions to the spin-1 Gross–Pitaevskii equation.

We establish a Lagrangian variational framework for general relativistic continuum theories that permits the development of the process of Lagrangian reduction by symmetry in the relativistic context. Starting with a continuum version of the Hamilton principle for the relativistic particle, we deduce two classes of reduced variational principles that are associated to either spacetime covariance, which is an axiom of the continuum theory, or material covariance, which is related to particular properties of the system such as isotropy. The covariance hypotheses and the Lagrangian reduction process are efficiently formulated by making explicit the dependence of the theory on given material and spacetime tensor fields that are transported by the world-tube of the continuum via the push-forward and pull-back operations. It is shown that the variational formulation, when augmented with the Gibbons–Hawking–York (GHY) boundary terms, also yields the Israel–Darmois junction conditions between the solution at the interior of the relativistic continua and the solution describing the gravity field produced outside from it. The expression of the first variation of the GHY term with respect to the hypersurface involves some extensions of previous results that we also derive in the paper. We consider in detail the application of the variational framework to relativistic fluids and relativistic elasticity. For the latter case, our setting also allows to clarify the relation between formulations of relativistic elasticity based on the relativistic right Cauchy-Green tensor or on the relativistic Cauchy deformation tensor. The setting developed here will be further exploited for modeling purpose in subsequent parts of the paper.

We consider a general regularized variational model for simulating wetting/dewetting phenomena arising from solids or fluids. The regularized model leads to the appearance of a precursor layer which covers the bare substrate, with the precursor height depending on the regularization parameter (varepsilon ). This model enjoys lots of advantages in analysis and simulations. With the help of the precursor layer, the spatial domain is naturally extended to a larger fixed one in the regularized model, which leads to both analytical and computational eases. There is no need to explicitly track the contact line motion, and difficulties arising from free boundary problems can be avoided. In addition, topological change events can be automatically captured. Under some mild and physically meaningful conditions, we show the positivity-preserving property of the minimizers of the regularized model. By using formal asymptotic analysis and (Gamma )-limit analysis, we investigate the convergence relations between the regularized model and the classical sharp-interface model. Finally, numerical results are provided to validate our theoretical analysis, as well as the accuracy and efficiency of the regularized model.

This paper is concerned with the convergence to sharp traveling waves of solutions with semi-compactly supported initial data for Burgers-Fisher-KPP equations with degenerate diffusion. We characterize the motion of the free boundary in the long-time asymptotic of the solution to Cauchy problem and the convergence to sharp traveling wave with almost exponential decay rates. Here a key difficulty lies in the intrinsic presence of nonlinear advection effect. After providing the analysis of the nonlinear advection effect on the asymptotic propagation speed of the free boundary, we construct sub- and super-solutions with semi-compact supports to estimate the motion of the free boundary. The new method overcomes the difficulties of the non-integrability of the generalized derivatives of sharp traveling waves at the free boundary.

Abstract

Starting from a classic non-local (in space) Cahn–Hilliard–Stokes model for two-phase flow in a thin heterogeneous fluid domain, we rigorously derive by mathematical homogenization a new effective mixture model consisting of a coupling of a non-local (in time) Hele-Shaw equation with a non-local (in space) Cahn–Hilliard equation. We then analyse the resulting model and prove its well-posedness. A key to the analysis is the new concept of sigma-convergence in thin heterogeneous domains allowing to pass to the homogenization limit with respect to the heterogeneities and the domain thickness simultaneously.

In this paper, we study the dynamics of a small rigid body in a viscous incompressible fluid in dimension two and three. More precisely we investigate the trajectory of the rigid body in the limit when its mass and its size tend to zero. We show that the velocity of the center of mass of the rigid body coincides with the background fluid velocity in the limit. We are able to consider the limit when the volume of the rigid bodies converges to zero while their densities are a fixed constant.

This paper is concerned with threshold dynamics of a degenerate diffusive HBV infection model with DNA-containing capsids in heterogeneous environment. We firstly address the existence of global solutions, uniform and ultimate boundedness of solutions, asymptotic smoothness of semiflows and existence of a connected global attractor for the diffusive model. Then, we identify the basic reproduction number ({mathcal {R}}_0) and establish a threshold-type result for the disease eradication or uniform persistence when ({mathcal {R}}_0le 1) or ({mathcal {R}}_0>1), respectively. Especially, when ({mathcal {R}}_0>1) and the diffusion rate of capsids or the diffusion rate of virions is zero, we further show that the model admits a unique infection steady state which is globally attractive. Our results indicate that the pathogen can be eliminated by limiting the mobility of the capsids or virions.

The parametric nonlinear Schrödinger equation models a variety of parametrically forced and damped dispersive waves. For the defocusing regime, we derive a normal velocity for the evolution of curved dark-soliton fronts that represent a (pi )-phase shift across a thin interface. We establish a simple mechanism through which the parametric term transitions the normal velocity evolution from a curvature-driven flow to motion against curvature regularized by surface diffusion of curvature. In the former case interfacial length shrinks, while in the latter case interface length generically grows until self-intersection followed by a transition to complex motion.