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CLASSIFICATIONS OF TWO-DIMENTIONAL HOMOGENEOUS CUBIC DIFFERENTIAL EQUATION SYSTEMS I
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Symmetric centers on planar cubic differential systems
Nonlinear Analysis, 2020The authors of this paper investigate the simultaneous existence of centers in symmetric planar polynomial differential systems. In particular, they present necessary and sufficient conditions for the existence of a bi-center of four families for real cubic symmetric systems and obtain the conditions for the isochronicity of such bi-centers.
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Local stability of cubic differential systems
ACM Communications in Computer Algebra, 2015Using Einstein’s notation [4]), the polynomial differential systems of finite dimension n and of degree at most k with coefficients in a field k of characteristic zero can be written as dx dt = a + ajα1x α1 + ajα1α2x 1x2 + ajα1···αrx α1 · · · xr (1) where j, α1, αr ∈ {1, . . . , n}, 1 ≤ r ≤ k, and for j = 1, . . . , n and for 2 ≤ r ≤ k, the tensor ajα1·
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Differential-flow-induced instability in a cubic autocatalator system
Journal of Engineering Mathematics, 1998The formation of spatio-temporal stable patterns is considered for a reaction-diffusion-convection system based upon the cubic autocatalator, \(A+2B\to 3B\), \(B\to C\), with the reactant \(A\) being replenished by the slow decay of some precursor \(P\) via the simple step \(P\to A\).
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