The cubic term in this equation becomes significant at densities on the order of \ frac { m ^ 2 } { \ kappa }.
2.
The smaller the cubic term is in relation to the gain, the more linear the device is, and the higher the TOI is, which clearly makes sense.
3.
In fact, the coefficient of cos ( " ?t " ) has nearly the same form as the transfer function, except for the factor ?on the cubic term.
4.
To see where these extra divisibility conditions come from, assume that " f " has a degenerate quadratic part " L " 2 and that " L " divides the cubic terms.
5.
Danca and Chen note that the Rabinovich Fabrikant system is difficult to analyse ( due to the presence of quadratic and cubic terms ) and that different attractors can be obtained for the same parameters by using different step sizes in the integration.
6.
If the quadratic term is negligible-- meaning that the linear term is sufficiently accurate without adding the quadratic term-- then linear interpolation is sufficiently accurate . ( If the problem is sufficiently important, or if the quadratic term is nearly big enough to matter, then one might want to determine whether the _ sum _ of the quadratic and cubic terms is large enough to matter in the problem .)
7.
The above solution shows that a quartic polynomial with rational coefficients and a zero coefficient on the cubic term is factorable into quadratics with rational coefficients if and only if either the resolvent cubic "'( " " ) "'has a non-zero root which is the square of a rational, or is the square of rational and 0 } }; this can readily be checked using the rational root test.
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