共查询到20条相似文献，搜索用时 15 毫秒
1.
研究差分方程χn+1=δχn-k+χn-k-1/A+χn-k-1,(n=0,1…)的全局性质。得到的结论是:若δ≤(A-1),方程的零平衡点全局渐进稳定;若A-1<δ≤A+1,方程的每个正解全局收敛于正平衡点。 相似文献
2.
In this paper, we present the preservation of a two-wing Lorenz-like attractor when in the Lorenz system a feedback control is applied, making two of its equilibria a sink. The forced system is capable of generating bistability and the trajectory settles down at one stable equilibrium point depending on the initial condition when the forced signal is zero. Due to a variation in the coupling strength of the control signal the symmetric equilibria of the Lorenz system move causing the basins of attraction to be the dynamic bounded regions that change accordingly. Thus, the preservation of a two-wing Lorenz-like attractor is possible using a switched control law between these dynamic basins of attraction. The forced switched systems also preserve multistability regarding the coupling strength and present multivalued synchronization according to the basin of attraction in which they were initialized. Bifurcations of the controlled system are used to exemplify the different basins generated by the forcing. An illustrative example is given to demonstrate the approach proposed. 相似文献
3.
Bifurcation theory is commonly used to study the dynamical behavior of ecosystems. It involves the analysis of points in the parameter space where the stability of the system changes qualitatively. The type of bifurcation that associates equilibria with periodic solution is called Hopf bifurcation. In this paper, a life energy system dynamic model of two components with multiple delays is presented. It is shown that the interaction parameters of the delayed ecosystem play a fundamental role in classifying the rich dynamics and bifurcation phenomena. Regarding the combined interaction parameter as a bifurcation parameter, the bifurcation values in the parameter plane are displayed. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by applying the normal form theory and the center manifold theorem. Moreover, the amplitudes of oscillations always increase as the interaction parameters increase, while the robustness of periods occurs as the interaction parameters vary. From an ecological point of view, the existence of Hopf bifurcation expresses periodic oscillatory behavior of the life energy system. 相似文献
4.
This paper investigates the chaos control problem of a new multi-scroll chaotic system. Two nonlinear control methods are studied, namely high-order and predictive types of control. The proposed methodologies offer the possibility of stabilizing unstable periodic orbits and unstable equilibrium points from the state equations. For this purpose, we apply the high-order control method for stabilizing a desired unstable periodic orbit, while the predictive control method is applied for stabilization problem of unstable equilibrium points. In particular, these approaches are effective and easy to be implemented since we only need to apply small perturbations to the system dynamics. The multi-scroll Chen system is used as representative example to show the working principle of these methods. Numerical simulation results indicate the potential engineering applications of the proposed control methods for various multi-scroll chaos-based practical applications. 相似文献
5.
蒋继发 《中国科学院研究生院学报》1991,(2)
在本文中,我们证明了R_ ~n上的合作和不可约向量场拥有一个处处非常数的不变函数的充要条件是奇点构成一条含原点的无界有序曲线;如果这样的不变函数存在,则每条有界轨线收敛于奇点。 相似文献
6.
《Journal of The Franklin Institute》2023,360(3):2068-2088
This article focuses on obtaining the solution of two-player zero-sum games (ZSGs) where the saddle point may not exist. From the standpoints of the upper performance index function (PIF) and lower PIF separately, we seek the solution of two-player differential ZSGs without assuming the strict existence of saddle point. To achieve the objective, we apply the generalized policy iteration (GPI) technique to design the controller. With neural network approximators, the system trajectory data are used to update the approximation of the PIFs. It is established that the upper (lower) PIF sequence is convergent along the iteration axis under the GPI scheme. When the two function sequences converge to equal values, the saddle point is attained, and vice versa. Numerical simulation results conformed to the suitability of the designed algorithm. 相似文献
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8.
Zhouchao Wei Amin Yousefpour Hadi Jahanshahi Uǧur Erkin Kocamaz Irene Moroz 《Journal of The Franklin Institute》2021,358(1):814-833
Having found hidden hyperchaos in a 5D self-exciting homopolar disc dynamo, we study the existence of a Hopf bifurcation, which leads to unstable limit cycles bifurcating from a stable equilibrium. Hidden chaos with only stable equilibria can be observed from the Hopf bifurcation: a typical way to enable hidden attractors to be located. We then provide a new fuzzy controller, and a fast fuzzy disturbance observer, based on terminal sliding mode control for synchronization of the hyperchaotic system. Fuzzy inference is considered to weaken the chattering phenomena. Using Lyapunov stability theory, the stability of the closed-loop system is proved. Finally, simulations of synchronization are illustrated to show the efficient performance of the designed control method via external disturbances and dynamic uncertainties. 相似文献
9.
A considerable body of literature has demonstrated-- empirically as well as analytically--that information systems need to be situated to the local context of use. Yet for infrastructural information systems that span numerous contexts spread out globally, this is literally prohibitive. For these systems to work, it is necessary to strike a balance between sensitiveness to local contexts and a need to standardize across contexts. We analyze a key element in this, namely, spelling out the (largely invisible) "costs" that the different actors pay to achieve working solutions. Empirically, we draw from an ongoing case study. We analyze the attempts of a maritime classification company with 5500 employees located in 300 sites in 100 countries to develop an infrastructural information system to support the surveying of ships globally. We elaborate design implications and concepts relevant to developing information infrastructures that also apply to the context of developing countries. 相似文献
10.
In the present paper, we study stochastic boundary control problems where the system dynamics is a controlled stochastic parabolic equation with Neumann boundary control and boundary noise. Under some assumptions, the continuity and differentiability of the value function are proved. We also define a new type of Hamilton–Jacobi–Bellman (HJB) equation and prove that the value function is a viscosity solution of this HJB equation. 相似文献
11.
In this paper, we develop a matrix-based methodology to investigate the problems of stability and stabilizability for a deterministic finite automaton (DFA) in the framework of the semi-tensor product (STP) of matrices. First, we discuss the equilibrium point stability (resp., set stability) of a DFA, i.e., verifying whether or not all state trajectories starting from a subset of states converge to a specified equilibrium point (resp., subset of states). The necessary and sufficient conditions for verifying both stabilities are given, respectively. Second, equilibrium point stabilizability (resp., set stabilizability) of a DFA is investigated as verifying the issue of whether or not a DFA can be globally or locally stabilized to a specified equilibrium point (resp., subset of states) by a permissible state-feedback controller. Based on the pre-reachability set and invariant-subset defined in this paper, the matrix-based criteria for verifying equilibrium point stabilizability and set stabilizability are derived, respectively. Furthermore, for each type of stabilizability, all permissible state-feedback controllers for the case of minimal length state trajectories, called optimal state-feedback controllers, are characterized by using the proposed polynomial algorithms. Finally, two examples are presented to illustrate the effectiveness of the theoretical results. 相似文献
12.
An impulsive reaction-diffusion periodic food-chain system with Holling type III functional response is presented and studied in this paper. Sufficient conditions for the ultimate boundedness and permanence of the food-chain system are established based on the upper and lower solution method and comparison theory of differential equation. By constructing appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Some numerical examples are shown to illustrate our results. A discussion is given in the end of the paper. 相似文献
13.
Aldo-Jonathan Muñoz-Vázquez Anand Sánchez-Orta Vicente Parra-Vega 《Journal of The Franklin Institute》2019,356(1):268-275
It is well known that a fractional-order system with a continuous right hand side does not have finite-time stable equilibria, but the discontinuous case has remained elusive in literature. Thus, based on novel mathematical tools, recently published in literature, it is demonstrated that attaining finite-time stable equilibria is not possible for a fractional-order system, not even in the case of an impulsive or discontinuous feedback. In consequence, it is demonstrated that, for a fractional-order system, a Lyapunov stable equilibrium cannot be at the same time finite-time stable. 相似文献
14.
《Journal of The Franklin Institute》2023,360(4):2421-2435
This paper studies the fault-tolerant control (FTC) problem of a class of strict-feedback nonlinear systems. First, we put forward a key theorem which shows that type-B Nussbaum functions can be extended to the cases containing multiple Nussbaum functions in the same Lyapunov inequality under certain conditions. Then, by using the techniques of Nussbaum functions and adaptive control, a new fault-tolerant control scheme is proposed. Compared with the previous work, this paper considers unknown time-varying control coefficients and unknown time-varying fault coefficients of actuators. It is proved that all the signals of the closed-loop system are globally bounded and the tracking error converges to zero asymptotically. Finally, simulations are provided to verify the effectiveness of the proposed control scheme. 相似文献
15.
In this paper, the asymptotic stability analysis is investigated for a kind of discrete-time bidirectional associative memory (BAM) neural networks with the existence of perturbations namely, stochastic, Markovian jumping and impulses. Based on the theory of stability, a novel Lyapunov–Krasovskii function is constructed and by utilizing the concept of delay partitioning approach, a new linear-matrix-inequality (LMI) based criterion for the stability of such a system is proposed. Furthermore, the derived sufficient conditions are expressed in the structure of LMI, which can be easily verified by a known software package that guarantees the globally asymptotic stability of the equilibrium point. Eventually, a numerical example with simulation is given to demonstrate the effectiveness and applicability of the proposed method. 相似文献
16.
《Journal of The Franklin Institute》2021,358(16):8656-8677
In this paper, a class of nonlocal Hopfield neural networks with random initial data is introduced, where the randomness may be of probability uncertainty. Sufficient conditions are derived to ensure the existence and globally exponential convergence of periodic solution for the addressed system in the frame of nonlinear expectation and linear expectation, respectively. Moreover, numerical examples are given to show the effectiveness of the obtained results. 相似文献
17.
A solution of the periodic problem in a nonlinear system comprising a single-valued symmetric nonlinearity (Lure system) and linear dynamics is presented. The solution is designed as an iterative application of Periodic Signal Mapping to refine the approximate solution obtained through the describing function method. The algorithm is based upon the transformation of the original nonlinear system into an equivalent nonlinear system for which the filtering hypothesis is satisfied exactly, and for that reason the latter being suitable for application of the developed algorithm. The solution sought for is a fixed point of the periodic signal mapping. Conditions of asymptotic convergence of the proposed algorithm are given. The proposed approach is illustrated by two examples of analysis of periodic motions in a relay feedback system and chattering in a terminal sliding mode. 相似文献
18.
This paper addresses the problem of local exponential stabilization via boundary feedback controllers for a class of nonlinear distributed parameter processes described by a scalar semi-linear parabolic partial differential equation (PDE). Both the domain-averaged measurement form and the boundary measurement form are considered. For the boundary measurement form, the collocated boundary measurement case and the non-collocated boundary measurement case are studied, respectively. For both domain-averaged measurement case and collocated boundary measurement case, a static output feedback controller is constructed. An observer-based output feedback controller is constructed for the non-collocated boundary measurement case. It is shown by the contraction semigroup theory and the Lyapunov’s direct method that the resulting closed-loop system has a unique classical solution and is locally exponentially stable under sufficient conditions given in term of linear matrix inequalities (LMIs). The estimation of domain of attraction is also discussed for the resulting closed-loop system in this paper. Finally, the effectiveness of the proposed control methods is illustrated by a numerical example. 相似文献
19.
In this paper, an eco-epidemiological model with time delay is considered. The asymptotical stability of the three equilibria, the existence of stability switches about both the disease-free planar equilibrium and the positive equilibrium are investigated. It is found that Hopf bifurcation occurs when the delay τ passes through a critical value. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations at the positive equilibrium are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given. 相似文献
20.
研究具有脉冲出生、脉冲接种和时滞的SEIRS传染病模型,分析无病周期解的存在性和全局稳定性,以及传染病模型的持久性,分析控制传染病传播的主要因素。 相似文献