For GGKdV equation, solutions of the compatible KdV equation are obtained by using CKdVE method, and Lie point symmetry group is also obtained. Further, some new exact non-traveling wave equivalent transformation method elliptic function on solving corresponding symmetric reduction local excitation modes three kinds under different groups parameters presented. Finally, integrability in sense CkdVE Symmetric proved, which shows effectiveness organic combination various nonlinear analytical...

In this paper, we study a stochastic predator–prey model with Beddington–DeAngelis functional response and Allee effect, show that there is unique global positive solution to the system initial value. Sufficient conditions for asymptotic stability are established. Some simulation figures introduced support analytical findings.

A generalized competitive system with stochastic perturbations is proposed in this paper, which the disturbances are described by famous Ornstein–Uhlenbeck process. By theories of differential equations, such as comparison theorem, Itô’s integration formula, Chebyshev’s inequality, martingale’s properties, etc., existence and uniqueness global positive solution obtained. Then sufficient conditions for extinction species almost surely, persistence mean permanence derived, respectively....

On the basis of simplest and deterministic chemostat model, we introduce impulsive input, nutrient recycling, distributed time-delay into model in this paper. By using comparison theorem, Floquet theory, small amplitude skills differential equation, it proves that if period input is too long parameter α kernel function delay small, then there exists a microorganism-eradication periodic solution globally asymptotically stable, cultivation microorganism fails. contrary, choose suitable...

In this paper, a simple direct method is presented to find equivalence transformation of nonlinear Whitham- Broer-Kaup equations. Applying transformation, we can obtain the symmetry group theorem Whitham-Broer-Kaup equations and then derive series new exact explicit solutions according previous references.

<abstract><p>In this paper, we study a food chain chemostat model with Michaelis-Menten function response and double delays. Applying the stability theory of functional differential equations, discuss conditions for three equilibria, respectively. Furthermore, analyze sufficient Hopf bifurcation system at positive equilibrium. Finally, present some numerical examples to verify correctness theoretical analysis give valuable conclusions further discussions end...

In this paper, we study an epidemic model with stage structure and latency spreading in a heterogeneous host population.We show that if the disease-free equilibrium exists, then global dynamics are determined by basic reproduction number R 0 .We prove is globally asymptotically stable when ≤ 1; there exists unique endemic which > 1.The stability of also proved using graph-theoretic approach to method Lyapunov functions.Finally, numerical simulations given illustrate main theoretical results.

Abstract This paper studies a stochastic differential equation SIS epidemic model, disturbed randomly by the mean-reverting Ornstein-Uhlenbeck process and Brownian motion. We prove existence uniqueness of positive global solutions model obtain controlling conditions for extinction persistence disease. The results show that when basic reproduction number Rs0 < 1, disease will extinct, on contrary, > persist. Furthermore, we can inhibit outbreak increasing intensity volatility or...

In this paper, a generalized nonautonomous stochastic competitive system with impulsive perturbations is studied. By the theories of differential equations and equations, we have established some asymptotic properties system, such as extinction, nonpersistence persistence in mean, weak permanence so on. order to show correctness feasibility theoretical results, several numerical examples are presented. Finally, effects different white noise discussed illustrated.

A nonautonomous epidemic prey-predator system with impulsive effects and multiple delays is considered; further, there an disease in the predator. By mean-value theorem of variables, integral inequalities, differential other mathematical analysis skills, sufficient conditions which guarantee permanence are obtained. Furthermore, by constructing a series Lyapunov functionals it proved that exists unique uniformly asymptotically stable almost periodic solution system.

In this paper, a stochastic SIS epidemic infectious diseases model with double perturbations is proposed. First, the existence and uniqueness of positive global solution are proved. Second, controlling conditions for extinction persistence disease obtained. Besides, effects intensity volatility [Formula: see text] speed reversion on dynamical behaviors discussed. Finally, some numerical examples given to support theoretical results. The results show that if basic reproduction number text],...

we give some new fixed point theorems for semi-closed 1-set-contractive operators and apply He's variational iteration method to solve integral equations (see [3]). We extend conclusion these methods are important meanings which different from the recent works.

We investigate the dynamics of a food-chain system with digest delay and periodic harvesting for prey. By using comparison theorem, small amplitude skills in impulsive differential equation, special qualitative analysis method we prove that there exists predators-eradication solution which is globally attractive show pest population can be controlled under economic threshold level uniformly permanent when harvest period<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"...

In this paper, a nonautonomous stochastic food-chain system with functional response and impulsive perturbations is studied. By using Itô’s formula, exponential martingale inequality, differential inequality other mathematical skills, some sufficient conditions for the extinction, nonpersistence in mean, persistence permanence of are established. Furthermore, asymptotic properties solutions also investigated. Finally, series numerical examples presented to support theoretical results,...

This paper analyzes the spread of COVID-19 epidemic in China, establishes a [Formula: see text] epidemiologic model that classifies diagnosed population into asymptomatic, mild, and severe, considers condition an isolated population. First all, we theoretically analyzed key problems disease-free equilibrium, stability, basic reproduction number model. Then, combined with actual data, development trend situation is simulated compared, influence some important parameters discussed evaluation...