Acta Applicandae Mathematicae最新文献

In this investigation, we delve into the dynamics of an ecoepidemic model, considering the intertwined influences of fear, refuge-seeking behavior, and alternative food sources for predators with selective predation. We extend our model to incorporate the impact of fluctuating environmental noise on system dynamics. The deterministic model undergoes thorough scrutiny to ensure the positivity and boundedness of solutions, with equilibria derived and their stability properties meticulously examined. Furthermore, we explore the potential for Hopf bifurcation within the system dynamics. In the stochastic counterpart, we prioritize discussions on the existence of a globally positive solution. Through simulations, we unveil the stabilizing effect of the fear factor on susceptible prey reproduction, juxtaposed against the destabilizing roles of prey refuge behavior and disease prevalence intensity. Notably, when disease prevalence intensity is too low, the infection can be eradicated from the ecosystem. Our deterministic analysis reveals a complex interplay of factors: the system destabilizes initially but then stabilizes as the fear factor suppressing disease prevalence intensifies, or as predators exhibit a stronger preference for infected prey over susceptible ones, or as predators are provided with more alternative food sources. Moreover, for the stochastic system, the oscillations tend to cluster around the coexistence equilibrium of the corresponding deterministic model when white noise intensity is low. However, with increasing white noise intensity, oscillation amplitudes escalate. Critically, very high levels of white noise can lead to the eradication of infection from the ecosystem.

We study the long-time behaviour of a run and tumble model which is a kinetic-transport equation describing bacterial movement under the effect of a chemical stimulus. The experiments suggest that the non-uniform tumbling kernels are physically relevant ones as opposed to the uniform tumbling kernel which is widely considered in the literature to reduce the complexity of the mathematical analysis. We consider two cases: (i) the tumbling kernel depends on the angle between pre- and post-tumbling velocities, (ii) the velocity space is unbounded and the post-tumbling velocities follow the Maxwellian velocity distribution. We prove that the probability density distribution of bacteria converges to an equilibrium distribution with explicit (exponential for (i) and algebraic for (ii)) convergence rates, for any probability measure initial data. To the best of our knowledge, our results are the first results concerning the long-time behaviour of run and tumble equations with non-uniform tumbling kernels.

Random Batch Methods (RBM) for mean-field interacting particle systems enable the reduction of the quadratic computational cost associated with particle interactions to a near-linear cost. The essence of these algorithms lies in the random partitioning of the particle ensemble into smaller batches at each time step. The interaction of each particle within these batches is then evolved until the subsequent time step. This approach effectively decreases the computational cost by an order of magnitude while increasing the amount of fluctuations due to the random partitioning. In this work, we propose a variance reduction technique for RBM applied to nonlocal PDEs of Fokker-Planck type based on a control variate strategy. The core idea is to construct a surrogate model that can be computed on the full set of particles at a linear cost while maintaining enough correlations with the original particle dynamics. Examples from models of collective behavior in opinion spreading and swarming dynamics demonstrate the great potential of the present approach.

The derivation of an approximate Class–I model for nonisothermal multicomponent systems of fluids, as the high-friction limit of a Class–II model is justified, by validating the Chapman–Enskog expansion performed from the Class–II model towards the Class–I model. The analysis proceeds by comparing two thermomechanical theories via relative entropy.

This work proposes a protocol for Fermionic Hamiltonian learning. For the Hubbard model defined on a bounded-degree graph, the Heisenberg-limited scaling is achieved while allowing for state preparation and measurement errors. To achieve (epsilon )-accurate estimation for all parameters, only (tilde{mathcal{O}}(epsilon ^{-1})) total evolution time is needed, and the constant factor is independent of the system size. Moreover, our method only involves simple one or two-site Fermionic manipulations, which is desirable for experiment implementation.

This paper concerns the polynomial decay of the dissipative wave equation subject to Kinetic boundary condition and non-neglected density in the square. After reformulating this problem into an abstract Cauchy problem, we show the existence and uniqueness of the solution. Then, by analyzing a family of eigenvalues of the corresponding operator, we prove that the rate of energy decay decreases in a polynomial way.

In this paper, we consider a system of two degenerate wave equations coupled through the velocities, only one of them being controlled. We assume that the coupling parameter is sufficiently small and we focus on null controllability problem. To this aim, using multiplier techniques and careful energy estimates, we first establish an indirect observability estimate for the corresponding adjoint system. Then, by applying the Hilbert Uniqueness Method, we show that the indirect boundary controllability of the original system holds for a sufficiently large time.

This paper is dedicated to studying the steady state problem of a population-toxicant model with negative toxicant-taxis, subject to homogeneous Neumann boundary conditions. The model captures the phenomenon in which the population migrates away from regions with high toxicant density towards areas with lower toxicant concentration. This paper establishes sufficient conditions for the non-existence and existence of non-constant positive steady state solutions. The results indicate that in the case of a small toxicant input rate, a strong toxicant-taxis mechanism promotes population persistence and engenders spatially heterogeneous coexistence (see, Theorem 2.3). Moreover, when the toxicant input rate is relatively high, the results unequivocally demonstrate that the combination of a strong toxicant-taxis mechanism and a high natural growth rate of the population fosters population persistence, which is also characterized by spatial heterogeneity (see, Theorem 2.4).

We deal with the following predator-prey model involving nonlinear indirect chemotaxis mechanism

under homogeneous Neumann boundary conditions in a bounded and smooth domain (Omega subset mathbb{R}^{n}) ((ngeq 1)), where the parameters (xi ,chi ,a_{1},a_{2},b_{1},b_{2},alpha ,beta ,gamma >0). It has been shown that if (r_{1}>1), (r_{2}>2) and (gamma (alpha +beta )<frac{2}{n}), then there exist some suitable initial data such that the system has a global classical solution ((u,v,w,z)), which is bounded in (Omega times (0,infty )). Compared to the previous contributions, in this work, the boundedness criteria are only determined by the power exponents (r_{1}), (r_{2}), (alpha ), (beta ), (gamma ) and spatial dimension (n) instead of the coefficients of the system and the sizes of initial data.

We consider in this paper numerical approximation and simulation of a two-species Keller-Segel model. The model enjoys an energy dissipation law, mass conservation and bound or positivity preserving for the population density of two species. We construct a class of very efficient numerical schemes based on the generalized scalar auxiliary variable with relaxation which preserve unconditionally the essential properties of the model at the discrete level. We conduct a sequence of numerical tests to validate the properties of these schemes, and to study the blow-up phenomena of the model in a three-dimensional domain in parabolic-elliptic form and parabolic-parabolic form.