Qualitative Theory of Dynamical Systems最新文献

The main result of this paper is to investigate the existence of a solution of a class of fractional problems involving the operator p-Laplacian with periodic potential and supercritical growth via the Mountain Pass theorem-Cerami version.

In this paper, we investigate the bifurcation, phase portrait and the traveling wave solutions of the coupled fractional Lakshmanan–Porsezian–Daniel equation by using the dynamical system bifurcation theory approach. Based on phase portrait, we obtain some new traveling wave solutions, which include Jacobi elliptic function solutions, soliton solutions, torsion wave solutions and periodic wave solutions. What’s more, we plot three-dimensional diagrams, contour plots and two-dimensional diagrams with the help of Maple, which provide a more visual demonstration of the section of this equation. The investigations are innovative and unexplored, and they can be employed to elucidate the physical phenomena that have been simulated, providing insights into their transient dynamic characteristics.

A stochastic toxin-mediated Lotka–Volterra competitive model with time-delay is formulated. Our primary goal is to study the impacts of white noise, environmental toxins and time-delay on population dynamics of the model. To begin with, we demonstrate that there exists a globally positive solution with the aid of constructing Lyapunov function. Then we discuss the uniform boundedness of the pth moment and invariant measure for the solution by Krylov–Bogoliubov theorem. Moreover, persistence and extinction are significant subjects in the study of biological population systems, so we further derive the sufficient conditions for weak persistence, persistence in time average and extinction of the solution, which can serve as a theoretical basis for protecting the diversity of aquatic organisms. In addition, using exponential martingale inequality and Borel–Cantelli lemma, the asymptotic pathwise estimation of system is given. Notably, we creatively explore the probability density function of the converted model, which is based on addressing the corresponding Fokker–Planck equation. In the end, utilizing computer simulation to illuminate the dominating results and reveal the influences of the above disturbances on the aquatic ecological population, such as high concentration of toxins can result in extinction, but a certain level of toxins can promote the persistence of highly resistant species.

This paper deals with a one-dimensional system in the linear isothermal theory of swelling porous elastic soils subject to fractional derivative-type boundary damping. We apply the semigroup theory. We prove well-posedness by the Lumer–Phillips theorem. We show the lack of exponential stability and strong stability is proved by using general criteria due to Arendt–Batty. Polynomial stability result is obtained by applying the Borichev–Tomilov theorem.

In this article, we present two novel ideas of f-contractions, named dual (f^{*})-weak rational contractions and triple (f^{*})-weak rational contractions, generalizing and expanding many of the solid results in this direction. The endeavor to apply the generalized Banach contraction principle to the set of f-contraction type mappings by applying numerous f-type functions gave rise to these novel generalizations. Also, under appropriate conditions, related unique fixed-point theorems are established. Moreover, some illustrative examples are given to support and strengthen the theoretical results. Furthermore, the obtained results are applied to discuss the existence of solutions to a fractional integral equation and a second-order differential equation. Finally, the significance of the new results and some future work are presented.

This work examines a discrete Leslie-Gower model of prey-predator dynamics with Holling type-IV functional response and harvesting effects. The study includes the existence and local stability analysis of all fixed points. Using center manifold theory, the codimension-1 bifurcations, viz. transcritical, Neimark–Sacker, fold, and period-doubling bifurcations, are determined for varying parameters. Moreover, the existence of codimension-2 Bogdanov–Takens bifurcation and Chenciner bifurcation is demonstrated, requiring two parameters to vary for the bifurcation to occur, and the non-degeneracy conditions for Bogdanov–Takens bifurcation are determined. An extensive numerical study is conducted to confirm the analytical findings. A wide range of dense, chaotic windows can be seen in the system, including period-2, 4, 8, and 16, period-doubling bifurcations, Neimark–Sacker bifurcations, and Chenciner and BT curves following two-parameters bifurcations. Further, it is also shown that the effect of harvesting parameter of the model for which the population dies out.

We investigate the existence of solutions for a class of fractional evolution equations with nonlocal initial conditions and superlinear growth nonlinear functions in Banach spaces. By using the compactness of semigroup generated by the linear operator, we neither assume any Lipschitz property of the nonlinear term nor the compactness of the nonlocal initial conditions. Moreover, the approximation technique coupled with the Hartmann-type inequality argument allows the treatment of nonlinear terms with superlinear growth. Then combining with the Leray-Schauder continuation principle, we prove the existence results. Finally, the results obtained are applied to fractional parabolic equations with continuous superlinearly growth nonlinearities and nonlocal initial conditions including periodic or antiperiodic conditions, multipoint conditions and integral-type conditions.

In this paper, we investigate the speed selection mechanism of traveling wave solutions for a reaction–diffusion–advection equation with high-order terms in a cylindrical domain. The study focuses the problem under two cases for Neumann boundary condition and Dirichlet boundary condition. By using the upper and lower solutions method, general conditions for both linear and nonlinear selections are obtained. When the equation is expanded to higher dimensions, literature examining this particular topic is scarce. In light of this, new results have been obtained for both linear and nonlinear speed selections of the equation with high-order terms. For different power exponents m and n, specific sufficient conditions for linear and nonlinear selections with the minimal wave speed are derived by selecting suitable upper and lower solutions. The impact of the power exponents m and n on speed selection is analyzed.

Abstract

There have been reports of influenza virus resistance in the past, and because this virus has the potential of resistance to cause several pandemics and also is lethal, we investigate the conditions under which the strains coexist as a result. The non-resistant strain undergoes mutation, giving rise to the resistant strain. The incidence rates of the non-resistant and saturated-resistant strains are bi-linear and saturated, respectively. In this study, two flu strain models (resistant and non-resistant) are investigated in a fractal–fractional sense, and the presence of solutions, stability, and numerical simulations are examined for various orders and derivative dimensions. Using numerical values from freely accessible open resources, a numerical technique that is based on Lagrange’s interpolation polynomial is constructed and validated for a particular example.

The aim of this work is to study the mild solutions for a class of impulsive neutral stochastic functional integrodifferential equations driven by fractional Brownian motion using noncompact semigroup in a Hilbert space. We assume that the linear part has a resolvent operator not necessarily compact but the operator norm is continuous. Sufficient conditions for the existence of mild solutions are obtained using the Hausdorff measure of noncompactness and the Mönch fixed point theorem. Furthermore, under some suitable assumptions, the considered system’s trajectory (T-) controllability is established using generalized Gronwall’s inequality. An example is delivered to illustrate the obtained theoretical results. Finally, real life fermentation example is discussed to supporting the proposed system.