Results 221 to 230 of about 8,492 (262)

On the Jacobian conjecture for global asymptotic stability

Journal of Dynamics and Differential Equations, 1992
An old conjecture says that, for the two-dimensional system of ordinary differential equations \(\dot x=f(x)\), where \(f:\mathbb{R}^ 2\to\mathbb{R}^ 2\), \(f\in C^ 1\), and \(f(0)=0\), the origin \(x=0\) should be globally asymptotically stable (i.e., a stable equilibrium and all trajectories \(x(t)\) converge to it as \(t\to+\infty)\) whenever the ...
Zampieri G, GORNI, Gianluca
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Global asymptotic stability of plant-seed bank models

Journal of Mathematical Biology, 2013
Many plant populations have persistent seed banks, which consist of viable seeds that remain dormant in the soil for many years. Seed banks are important for plant population dynamics because they buffer against environmental perturbations and reduce the probability of extinction.
Eager, Eric Alan, Rebarber, Richard, Tenhumberg, Brigitte   +2 more
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Global Asymptotic Stability of Delayed Cellular Neural Networks

IEEE Transactions on Neural Networks, 2007
A new criterion for the global asymptotic stability of the equilibrium point of cellular neural networks with multiple time delays is presented. The obtained result possesses the structure of a linear matrix inequality and can be solved efficiently using the recently developed interior-point algorithm.
Huaguang, Zhang, Zhanshan, Wang
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Global Asymptotic Stability for Oscillators with Superlinear Damping

Journal of Dynamics and Differential Equations, 2012
The authors study the global asymptotic stability of the equilibrium for the damped superlinear oscillator \[ x''+a(t) \varphi_q(x') +\omega^2 x=0.
Sugie, Jitsuro, Shimadu, Tsunehiko, Yamasaki, Takashi   +2 more
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Global asymptotic stability in pseudolinear systems

Mathematical Notes, 2017
The author gives a counterexample to a theorem on global asymptotic stability published by \textit{S. P. Banks} and \textit{K. J. Mhana} [IMA J. Math. Control Inf. 9, No. 2, 179--196 (1992; Zbl 0773.49018)].
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Global asymptotic stability for two recursive difference equations

Applied Mathematics and Computation, 2004
The authors study the global asymptotic stability of the following two recursive difference equations \[ x_{n+1}=\frac{x_nx_{n-1}+x_{n-1}+a}{x_n+x_{n-1}x_{n-2}+a},\text{ } n=0,1,2,..., \] and \[ x_{n+1}=\frac{x_{n-1}+x_nx_{n-2}+a}{x_nx_{n-1}+x_{n-2}+a},\text{ } n=0,1,2,..., \] where \(a\in [0,\infty )\) and the initial values \(x_{-2},x_{-1},x_0\in (0,\
Li, Xianyi, Zhu, Deming
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Global Asymptotic Stabilization Using Adaptive Fuzzy PD Control

IEEE Transactions on Cybernetics, 2015
It is well-known that standard adaptive fuzzy control (AFC) can only guarantee uniformly ultimately bounded stability due to inherent fuzzy approximation errors (FAEs). This paper proves that standard AFC with proportional-derivative (PD) control can guarantee global asymptotic stabilization even in the presence of FAEs for a class of uncertain affine ...
null Yongping Pan, null Haoyong Yu, null Tairen Sun   +2 more
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Global asymptotic stability and global exponential stability of delayed cellular neural networks

IEEE Transactions on Circuits and Systems II: Express Briefs, 2005
In this brief, many novel theorems and corollaries are presented regarding the global asymptotic stability and global exponential stability of cellular neural networks with constant and variable time delays. The stability conditions in the new results improve and generalize existing ones.
X.X. Liao, null Jun Wang, null Zhigang Zeng   +2 more
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Global asymptotical stability and global finite-time stability for nonlinear homogeneous systems

IFAC Proceedings Volumes, 2011
Abstract In this paper, we investigate global asymptotical stability and global finite-time stability for a class of nonlinear homogeneous systems with different degree of homogeneity which can be greater or less than 0, respectively. The results are obtained by the property of homogeneity and local behaviour near the origin.
Yanjun Shen, Xiaohua Xia
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Global Asymptotic Stability and Stabilization of Neural Networks With General Noise

IEEE Transactions on Neural Networks and Learning Systems, 2018
Neural networks (NNs) in the stochastic environment were widely modeled as stochastic differential equations, which were driven by white noise, such as Brown or Wiener process in the existing papers. However, they are not necessarily the best models to describe dynamic characters of NNs disturbed by nonwhite noise in some specific situations.
Qihe Shan, Huaguang Zhang, Zhanshan Wang, Zhao Zhang   +3 more
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