New sufficient conditions for a center and global phase portraits for polynomial systems
Copyright policy )New sufficient conditions for a center and global phase portraits for polynomial systems
The authors consider a system \[ x'=P(x,y),\quad y'=Q(x,y), \] where \(P,Q\) are polynomials in \(x,y\). They study the function \(1/M(x,y)\) (where \(M\) is an integrating factor for the system) to find new explicit conditions under which the system has a center. For cubic systems, global phase portraits in the case of center existence are described.
cubic systems, integrating factor, center, Bifurcations of limit cycles and periodic orbits in dynamical systems, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, global phase portraits
cubic systems, integrating factor, center, Bifurcations of limit cycles and periodic orbits in dynamical systems, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, global phase portraits
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