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1.IntroductionPartialdifferenceequationshaveappearedinmanybranchesofmathematics.Indeed,LagrangeandLaplacehavediscussedsuchequationsinrelationtoprobability[1],Couralltetal.[z]haveconsideredtheminrelationtodifferentialequationsofmathematicalphysics.Inrecenty6ars,signalandimageprocessingtheory(seee.g.[3])alsomakesuseofthetheoryofpartialdchrenceequations.OscillationtheoryfortheseeqllationshasbeeninvestigatedbyanUmberofauthorsrecelltly[4].However,asystematicinvestigationofthestabilitytheoryofpart… 相似文献
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Hideaki Matsunaga 《Proceedings of the American Mathematical Society》2008,136(12):4305-4312
For a linear delay differential system with two coefficients and one delay, we establish some necessary and sufficient conditions on the asymptotic stability of the zero solution, which are composed of delay-dependent and delay-independent stability criteria. On the former criterion, the range of the delay is explicitly given.
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Yoshiaki Muroya Emiko Ishiwata Nicola Guglielmi 《Journal of Mathematical Analysis and Applications》2007,334(1):232-247
Consider the following nonlinear difference equation with variable coefficients:
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Hodgkin-Huxley系统的渐进稳定性 总被引:1,自引:1,他引:0
李全国 《纯粹数学与应用数学》2008,24(2)
用无穷维动力系统的方法研究了Hodgkin-Huxley神经脉冲传导系统的长时间行为.在齐次边界条件与非齐次边界条件证明了系统在其不变流形上的全局吸引子为系统在该不变流形内的唯一平衡点,从而证明了该系统的渐进稳定性. 相似文献
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Bratislav D. Iri?anin 《Applied mathematics and computation》2010,216(4):1325-4324
We give elegant and short proofs of some recent results on global stability of some classes of higher-order nonlinear difference equations. 相似文献
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This work examines the stability of explicit Runge-Kutta methods applied to a certain linear ordinary differential equation with periodic coefficients. On this problem naïve use of the eigenvalues of the Jacobian results in misleading conclusions about stable behaviour. It is shown, however, that a valid analogue of the classical absolute stability theory can be developed. Further, using a suitable generalisation of the equilibrium theory of Hall [ACM Trans. on Math. Soft. 11 (1985), pp. 289–301], accurate predictions are made about the performance of modern, adaptive algorithms.Supported by the University of Dundee Research Initiatives Fund. 相似文献
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非线性时滞差分议程的全局渐近稳定性 总被引:1,自引:0,他引:1
In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained,xn 1=xn xn-1xn-2 a/xmxm-1 xn-2 a,n=0,1…,where a∈(0,∞) and the initial values x-2,x-1,x0∈(0,∞).As a special case,a conjecture by Ladas is confirmed. 相似文献
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The problem of optimal fixed-time controllability to zero for an ordinary differential equation is investigated. We were inspired by the papers Lopez-Ramirez et al. (2018) and Polyakov (2012). We assume that our system is finite time stable. The initial conditions of trajectories we treat as control. We want to maximize the time when the trajectory starting at initial condition terminates at zero. We continue the control approach to stability from Polyakov (2012) to construct sufficient optimality conditions for the fixed-time stability in terms of the optimal control theory and find closed-loop control (feedback control) to steer the trajectory to zero. 相似文献
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Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its
two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy
uniformly bounded by exponentially decaying function of time. The result is achieved by considering an energy-like Lyapunov
functional for the system. 相似文献
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This paper is concerned with a class of systems of delay differential equations which are defined on the nonnegative function space. Under proper conditions, we employ a novel proof to establish several criteria of the global stability of positive equilibrium. Moreover, we give two examples to illustrate our main results. 相似文献
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This paper is concerned with delay-independent asymptotic stability of a numerical process that arises after discretization
of a nonlinear one-dimensional diffusion equation with a constant delay by the Euler method. Explicit sufficient and necessary
conditions for the Euler method to be asymptotically stable for all delays are derived. An additional restriction on spatial
stepsize is required to preserve the asymptotic stability due to the presence of the delay. A numerical experiment is implemented
to confirm the results.
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In this paper, we generalize some integral inequalities to more general situations, and the inequalities of Pachpatte type are corollaries of our's. We establish bounds on the solutions, and we show the usefulness of our results in investigating the asymptotic behavior and the stability on the solutions of integral equations, differential equations and integro-differential equations with time delay. 相似文献
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In this paper, we give some sufficient conditions to guarantee global asymptotic stability of the zero solution of the third‐order nonlinear differential equation: x ′ ′ ′ + g(x,x ′ ,x ′ ′ ) + f(x,x ′ )x ′ + h(x) = 0. Two examples are also given to illustrate our results. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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熊双平 《纯粹数学与应用数学》2005,21(1):39-45
研究了一类非线性有限时滞脉冲泛函微分系统,利用比较原理和Lyapunov函数,得到了系统零解一致最终稳定性及一致最终渐近稳定性的充分条件. 相似文献
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N. O. Sedova 《Russian Mathematics (Iz VUZ)》2008,52(11):60-69
We study certain sufficient conditions for the local and global uniform asymptotic stability, as well as the stabilizability of the equilibrium in cascade systems of delay differential equations. As distinct from the known results, the assertions presented in this paper are also valid for the cases, when the right-hand sides of equations are nonlinear and depend on time or arbitrarily depend on the historical data of the system. We prove that the use of auxiliary constant-sign functionals and functions with constant-sign derivatives essentially simplifies the statement of sufficient conditions for the asymptotic stability of a cascade. We adduce an example which illustrates the use of the obtained results. It demonstrates that the proposed procedure makes the study of the asymptotic stability and the construction of a stabilizing control easier in comparison with the traditional methods. 相似文献
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Xin Liu Lili Chen Yanfeng Zhao Xianhua Song 《Mathematical Methods in the Applied Sciences》2022,45(1):77-92
In this paper, the problem of the uniform stability for a class of fuzzy fractional-order genetic regulatory networks with random discrete delays, distributed delays, and parameter uncertainties is studied. Although there is a portion of literature on using fixed point theorems to study the stability of fractional neural networks, most of them required the fractional order to be in . However, the case of the fractional-order belonging to has not been discussed. To solve it, this work proposes a novel idea of using fixed point theory to study the stability of fuzzy (0,1) order neural networks, the problem of the uniqueness of the solution of the considered genetic regulatory networks is resolved, and a novel sufficient condition to guarantee the uniform stability of above genetic regulatory networks is also derived. Eventually, an example is given to demonstrate that the obtained result is effective. 相似文献