Mean Dimension for Non-autonomous Iterated Function Systems

In this paper we introduce the notions of mean dimension and metric mean dimension for non-autonomous iterated function systems(NAIFSs for short)on countably infinite alphabets which can be regarded as generalizations of the mean dimension and the Lindenstrauss metric mean dimension for non-autonomous iterated function systems.We also show the relationship between the mean topological dimension and the metric mean dimension.

Permanence and Global Stability for a Non-Autonomous Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes with Delays

In this paper, a nonautonomous predator-prey system based on a modified version of the Leslie-Gower scheme and Holling-type II scheme with delayed effect is investigated. The general criteria of integrable form on the permanence are established. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for global stability of any positive solutions to the

Existence of Solutions for a Non-Autonomous Evolution Equations with Nonlocal Conditions

The existence of mild solutions for non-autonomous evolution equations with nonlocal conditions in Banach space is studied in this article. We obtained the existence of at least one mild solution to the evolution equations by using Krasnoselskii’s fixed point theorem as well as the theory of the evolution family. The interest of this paper is that any assumptions are not imposed on the nonlocal terms and Green’s functions and a new alternative method is applied to prove the existence of mild solutions. The results obtained in this paper may improve some related conclusions on this topic. An example is given as an application of the results.

THE PERSISTENCE OF SOLUTIONS IN A NONLOCAL PREDATOR-PREY SYSTEM WITH A SHIFTING HABITAT

In this paper,we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment.It is known that Choi et al.[J Differ Equ,2021,302:807-853]studied the persistence or extinction of the prey and of the predator separately in various moving frames.In particular,they achieved a complete picture in the local diffusion case.However,the question of the persistence of the prey and of the predator in some intermediate moving frames in the nonlocal diffusion case was left open in Choi et al.'s paper.By using some a prior estimates,the Arzelà-Ascoli theorem and a diagonal extraction process,we can extend and improve the main results of Choi et al.to achieve a complete picture in the nonlocal diffusion case.

Persistence in Non-Autonomous Lotka-Volterra System with Predator-Prey Ratio-Dependence and Density Dependence

The main purpose of this article is considering the persistence non-autonomous Lotka-Volterra system with predator-prey ratio-dependence and density dependence. We get the sufficient conditions of persistence of system, further have the necessary conditions, also the uniform persistence condition, which can be easily checked for the model is obtained.

Qualitative Properties of Equilibrium Point in a Discrete Predator-Prey Model

In this paper, the dynamic properties of a discrete predator-prey model are discussed. The properties of non-hyperbolic fixed points and hyperbolic fixed points of the model are analyzed. First, by using the classic Shengjin formula, we find the existence conditions for fixed points of the model. Then, by using the qualitative theory of ordinary differential equations and matrix theory we indicate which points are hyperbolic and which are non-hyperbolic and the associated conditions.

Uniform attractors for non-autonomous Klein-Gordon-Schrdinger lattice systems

The existence of a compact uniform attractor for a family of processes corre- sponding to the dissipative non-autonomous Klein-Gordon-SchrSdinger lattice dynamical system is proved. An upper bound of the Kolmogorov entropy of the compact uniform attractor is obtained, and an upper semicontinuity of the compact uniform attractor is established.

Finite-time stabilization of uncertain non-autonomous chaoticgyroscopes with nonlinear inputs

Gyroscopes are one of the most interesting and everlasting nonlinear nonautonomous dynamical systems that exhibit very complex dynamical behavior such as chaos. In this paper, the problem of robust stabilization of the nonlinear non-autonomous gyroscopes in a given finite time is studied. It is assumed that the gyroscope system is perturbed by model uncertainties, external disturbances, and unknown parameters. Besides, the effects of input nonlinearities are taken into account. Appropriate adaptive laws are proposed to tackle the unknown parameters. Based on the adaptive laws and the finite-time control theory, discontinuous finite-time control laws are proposed to ensure the finite-time stability of the system. The finite-time stability and convergence of the closed-loop system are analytically proved. Some numerical simulations are presented to show the efficiency of the proposed finite-time control scheme and to validate the theoretical results.

Adaptive coupled synchronization of non-autonomous systems in ring networks

The adaptive coupled synchronization method for non-autonomous systems is proposed. This method can avoid estimating the value of coupling coefficient. Under the uniform Lipschitz assumption, we derive the asymptotical synchronization for a general coupling ring network with N identical non-autonomous systems~ even when N is large enough. Strict theoretical proofs are given. Numerical simulations illustrate the effectiveness of the present method.

Design of an adaptive finite-time controller for synchronization of two identical/different non-autonomous chaotic flywheel governor systems

The centrifugal flywheel governor （CFG） is a mechanical device that automatically controls the speed of an engine and avoids the damage caused by sudden change of load torque. It has been shown that this system exhibits very rich and complex dynamics such as chaos. This paper investigates the problem of robust finite-time synchronization of non-autonomous chaotic CFGs. The effects of unknown parameters, model uncertainties and external disturbances are fully taken into account. First, it is assumed that the parameters of both master and slave CFGs have the same value and a suitable adaptive finite-time controller is designed. Second, two CFGs are synchronized with the parameters of different values via a robust adaptive finite-time control approach. Finally, some numerical simulations are used to demonstrate the effectiveness and robustness of the proposed finite-time controllers.

Non-autonomous discrete Boussinesq equation:Solutions and consistency

A non-autonomous 3-component discrete Boussinesq equation is discussed. Its spacing parameters Pn and qm are related to independent variables n and m, respectively. We derive bilinear form and solutions in Casoratian form. The plain wave factor is defined through the cubic roots of unity. The plain wave factor also leads to extended non-autonomous discrete Boussinesq equation which contains a parameter δ. Tree-dimendional consistency and Lax pair of the obtained equation are discussed.

Some results on entropy dimension for non-autonomous systems

In this paper,the preimage branch t-entropy and entropy dimension for nonautonomous systems are studied and some systems with preimage branch t-entropy zero are introduced.Moreover,formulas calculating the s-topological entropy of a sequence of equi-continuous monotone maps on the unit circle are given.Finally,examples to show that the entropy dimension of non-autonomous systems can be attained by any positive number s are constructed.

A fast computing method to distinguish the hyperbolic trajectory of an non-autonomous system

Attempting to find a fast computing method to DHT （distinguished hyperbolic trajectory）, this study first proves that the errors of the stable DHT can be ignored in normal direction when they are computed as the trajectories extend. This conclusion means that the stable flow with perturbation will approach to the real trajectory as it extends over time. Based on this theory and combined with the improved DHT computing method, this paper reports a new fast computing method to DHT, which magnifies the DHT computing speed without decreasing its accuracy.

Pullback Attractor of a Non-autonomous Model for Epitaxial Growth

In this paper, we consider a non-autonomous model for epitaxial growth. It is shown that a pullback attractor of the model exists when the external force has exponential growth.

Global Attractor for a Non-Autonomous Beam Equation

This work studies the global attractor for the process generated by a non-autonomous beam equation utt+△2u+ηut-[β(t)+M(∫Ω|▽u(x,t)|2dx)] △u+g(u, t)=f (x,t) Based on a time-uniform priori estimate method, we first in the space H02(Ω) ×L2(Ω) establish a time-uniform priori estimate of the solution u to the equation, and conclude the existence of bounded absorbing set. When the external term f (x,t) is time-periodic, the continuous semigroup of solution is proved to possess a global attractor.

Modified Lindstedt-Poincaré Method for Obtaining Resonance Periodic Solutions of Nonlinear Non-autonomous Oscillators

A modified Lindstedt-Poincar＆#233; （LP） method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomous equa-tions are converted into a group of linear ordinary differential equations by introducing a set of simple transformations. An approximate resonance solution for the original equation can then be obtained. The periodic solutions of primary, super-harmonic, sub-harmonic, zero-frequency and combination resonances can be solved effectively using the modi-fied method. Some examples, such as damped cubic nonlinear systems under single and double frequency excitation, and damped quadratic nonlinear systems under double frequency excitation, are given to illustrate its convenience and effectiveness. Using the modified LP method, the first-order approximate solutions for each equation are obtained. By comparison, the modified method proposed in this paper produces the same results as the method of multiple scales.

ON EXPONENTIAL STABILITY OF NON-AUTONOMOUS STOCHASTIC SEMILINEAR EVOLUTION EQUATIONS

Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approximating solution systems and usig a limiting argument to pass on stability of strong solutions to mild ones. Consequently, under these conditions the random attractors of given stochastic systems are reduced to zero with exponential decay. Lastly, two examples are investigated to illustrate the theory.

Pullback Random Attractors for Non-Autonomous Stochastic Fractional FitzHugh-Nagumo System

This paper is concerned with the asymptotic behavior of solutions for a class of non-autonomous fractional FitzHugh-Nagumo equations deriven by additive white noise. We first provide some sufficient conditions for the existence and uniqueness of solutions, and then prove the existence and uniqueness of tempered pullback random attractors for the random dynamical system generated by the solutions of considered equations in an appropriate Hilbert space. The proof is based on the uniform estimates and the decomposition of dynamical system.

Persistence and Extinction of a Non-Autonomous Plant Disease Model with Roguing^*

On the basis of analyzing the shortages of present studies on plant disease model for autonomous phenomenon, and considering the actual situation, this paper applies the joint factors of environmental change and the infectivity for latent plants into the system;therefore we deal with a non-autonomous plant disease model with roguing. Some sufficient conditions are established for extinction of diseases and permanence of the system in this paper.

Finite Fractal Dimensionality of Compact Kernel Sections for Dissipative Non-Autonomous Klein-Gordon-Schrödinger Lattice Systems

In this paper, an upper bound of fractal dimension of the compact kernel sections for the dissipative non-autonomous Klein-Gordon-Schrödinger lattice system is obtained, by applying a criterion for estimating fractal dimension of a family of compact subsets of a separable Hilbert space.