Attractor of a nonlinear hybrid reaction–diffusion model of neuroendocrine transdifferentiation of human prostate cancer cells with time-lags

Prostate cancer is a serious disease that endangers men's health. The genetic mechanism and treatment of prostate cancer have attracted the attention of scientists. In this paper, we focus on the nonlinear mixed reaction diffusion dynamics model of neuroendocrine transdifferentiation of prostate cancer cells with time delays, and reveal the evolutionary mechanism of cancer cells mathematically. By applying operator semigroup theory and the comparison principle of parabolic equation, we study the global existence, uniqueness and boundedness of the positive solution for the model. Additionally, the global invariant set and compact attractor of the positive solution are obtained by Kuratowski's measure of noncompactness. Finally, we use the Pdepe toolbox of MATLAB to carry out numerical calculations and simulations on an example to check the correctness and effectiveness of our main results. Our results show that the delay has no effect on the existence, uniqueness, boundedness and invariant set of the solution, but will affect the attractor

2 n positive periodic solutions to n species non‐autonomous Lotka‐volterra unidirectional food chains with harvesting terms

By using the Mawhin continuation theorem of coincidence degree theory and some results on inequalities, we establish the existence of 2 n positive periodic solutions for n species non‐autonomous Lotka‐Volterra unidirectional food chains with harvesting terms. Two examples are given to illustrate the effectiveness of our results. First published online: 09 Jun 201

The relationship between childhood trauma and Internet gaming disorder among college students: A structural equation model

open access journalBackground The aim of this study was to investigate the mechanisms of Internet gaming disorder (IGD) and the associated interaction effects of childhood trauma, depression and anxiety in college students. Methods Participants were enrolled full-time as freshmen at a University in the Hunan province, China. All participants reported their socio-demographic characteristics and undertook a standardized assessment on childhood trauma, anxiety, depression and IGD. The effect of childhood trauma on university students' internet gaming behaviour mediated by anxiety and depression was analysed using structural equation modelling (SEM) using R 3.6.1. Results In total, 922 freshmen participated in the study, with an approximately even male-to-female ratio. A mediation model with anxiety and depression as the mediators between childhood trauma and internet gaming behaviour allowing anxiety and depression to be correlated was tested using SEM. The SEM analysis revealed that a standardised total effect of childhood trauma on Internet gaming was 0.18, (Z = 5.60, 95% CI [0.02, 0.05], P < 0.001), with the direct effects of childhood trauma on Internet gaming being 0.11 (Z = 3.41, 95% CI [0.01, 0.03], P = 0.001), and the indirect effects being 0.02 (Z = 2.32, 95% CI [0.00, 0.01], P = 0.020) in the pathway of childhood trauma-depression-internet gaming; and 0.05 (Z = 3.67, 95% CI [0.00, 0.02], P < 0.001) in the pathway of childhood trauma-anxiety-Internet gaming. In addition, the two mediators anxiety and depression were significantly correlated (r = 0.50, Z = 13.54, 95% CI [3.50, 5.05], P < 0.001). Conclusions The study revealed that childhood trauma had a significant impact on adolescents' Internet gaming behaviours among college students. Anxiety and depression both significantly mediated the relationship between childhood trauma and internet gaming and augmented its negative influence. Discussion of the need to understand the subtypes of childhood traumatic experience in relationship to addictive behaviours is included

Solvability, Approximation and Stability of Periodic Boundary Value Problem for a Nonlinear Hadamard Fractional Differential Equation with <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">p</mi></mrow></semantics></math></inline-formula>-Laplacian

The fractional order p-Laplacian differential equation model is a powerful tool for describing turbulent problems in porous viscoelastic media. The study of such models helps to reveal the dynamic behavior of turbulence. Therefore, this article is mainly concerned with the periodic boundary value problem (BVP) for a class of nonlinear Hadamard fractional differential equation with p-Laplacian operator. By virtue of an important fixed point theorem on a complete metric space with two distances, we study the solvability and approximation of this BVP. Based on nonlinear analysis methods, we further discuss the generalized Ulam-Hyers (GUH) stability of this problem. Eventually, we supply two example and simulations to verify the correctness and availability of our main results. Compared to many previous studies, our approach enables the solution of the system to exist in metric space rather than normed space. In summary, we obtain some sufficient conditions for the existence, uniqueness, and stability of solutions in the metric space

Existence of positive periodic solutions for the impulsive Lotka–Volterra cooperative population model with time-delay and harvesting control on time scales

Abstract In this paper, we consider a class of impulsive Lotka–Volterra cooperative population models with time delay and harvesting control on time scales. Using the fixed point theorem of strict-set-contraction, we analyze the existence conditions of positive periodic solutions for this model. As applications, we analyze the existence conditions of positive periodic solutions for some common Lotka–Volterra systems on time scales

Stability of a Nonlinear Langevin System of ML-Type Fractional Derivative Affected by Time-Varying Delays and Differential Feedback Control

The Langevin system is an important mathematical model to describe Brownian motion. The research shows that fractional differential equations have more advantages in viscoelasticity. The exploration of fractional Langevin system dynamics is novel and valuable. Compared with the fractional system of Caputo or Riemann–Liouville (RL) derivatives, the system with Mittag–Leffler (ML)-type fractional derivatives can eliminate singularity such that the solution of the system has better analytical properties. Therefore, we concentrate on a nonlinear Langevin system of ML-type fractional derivatives affected by time-varying delays and differential feedback control in the manuscript. We first utilize two fixed-point theorems proposed by Krasnoselskii and Schauder to investigate the existence of a solution. Next, we employ the contraction mapping principle and nonlinear analysis to establish the stability of types such as Ulam–Hyers (UH) and Ulam–Hyers–Rassias (UHR) as well as generalized UH and UHR. Lastly, the theoretical analysis and numerical simulation of some interesting examples are carried out by using our main results and the DDESD toolbox of MATLAB

Global exponential stability of positive almost periodic solutions for a class of two-layer Gilpin–Ayala predator–prey model with time delays

Abstract This paper mainly considers a class of two-layer Gilpin–Ayala predator–prey models with time delays. By means of Mawhin’s continuation theorem of coincidence degree theory, some new sufficient criteria for the existence of positive almost periodic solutions have been established. We also obtain the global exponential stability of the positive almost periodic solution for this system by constructing appropriate Lyapunov functionals and smart transformations. As an application, an example is given to illustrate the validity of our main results