Results 251 to 260 of about 658,341 (287)

Polynomial first integrals for quasi-homogeneous polynomial differential systems

Nonlinearity, 2002
Here, several results concerning first integrals of homogeneous polynomial systems of differential equations are generalized to quasi-homogeneous polynomial systems. Properties of such systems are characterized in terms of the eigenvalues of the associated Kowalevskaya matrix.
Llibre, Jaume, Zhang, Xiang
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A Hybrid Polynomial System Solving Method for Mixed Trigonometric Polynomial Systems

SIAM Journal on Numerical Analysis, 2008
Mixed trigonometric polynomial systems arise in many fields of science and engineering. Commonly, this class of systems is transformed into polynomial systems by variable substituting and adding some quadratic equations, and then solved by some polynomial system solving method.
Bo Yu, Bo Dong
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Stability of Polynomial Systems via Polynomial Lyapunov Functions

2007 Chinese Control Conference, 2006
The stability of a class of polynomial systems is investigated by constructing a polynomial Lyapunov function. The key technique is to convert the polynomial Lyapunov candidate and it derivative into formal quadratic forms and to test their positivity and negativity respectively.
Qi Hongsheng, Cheng Daizhan
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Quasi-polynomial Systems

1995
Numerical or analytical investigation of systems of differential equations is usually greatly facilitated if the right-hand sides of the equations are polynomials with respect to the unknown functions (polynomial systems). Such systems occur quite naturally in celestial mechanics in dealing with solutions in the vicinity of some known particular ...
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A Polynomial Membership Function Approach for Stability Analysis of Fuzzy Systems

IEEE Transactions on Fuzzy Systems, 2021
Wen-Bo Xie, Hak-Keung Lam, Jian Zhang
exaly  

Strategies for Polynomial Systems

2009
Before we devote numerous pages to the topic of polynomial systems of equations over finite fields, we should pause and ask why one would want to do this. This will give us an opportunity to highlight the several applications of this interesting area.
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Systems and Polynomial Matrices

1980
The usual starting-point for a theory of time-invariant, finite-dimensional linear systems is $${}_{{y = Cx}}^{{\dot{x} = Ax + Bu}}\}$$ (1) but for certain purposes this is too restrictive.
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DA in Polynomial Systems

2011
This chapter addresses the estimation of the DA of equilibrium points of polynomial systems, i.e. dynamical systems whose dynamics is described by a polynomial function of the state, by using polynomial LFs and SOS programming. It is shown that a condition for establishing whether a sublevel set of a LF is an estimate of the DA can be obtained in terms
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Optimal sparse polynomial chaos expansion for arbitrary probability distribution and its application on global sensitivity analysis

Computer Methods in Applied Mechanics and Engineering, 2022
Jie Liu
exaly  

Reliability analysis using adaptive Polynomial-Chaos Kriging and probability density evolution method

Reliability Engineering and System Safety, 2022
Yongbo Peng
exaly