Generating limit cycles from a nilpotent critical point via normal forms

Limit Cycles and Integrability in a Class of Systems with High-Order Nilpotent Critical Points

and Applied Analysis 3 Thus, the origin of system (13) is an element critical point. It could be investigated using the classical integral factor method. Now, we consider the following system: dx dt = y + A30x3n + A21x2ny + A12xny2 + A03y3, dy dt = −x2n−1 + xn−1 (B30x3n + B21x2ny + B12xny2 + B03y3) . (14) When n = 2k + 1, by those transformations, system (14) is changed into dx dt = −y − √2k + ...

stable limit cycles generating in a class of uncertain nonlinear systems: application in inertia pendulum

this paper considers the problem of stable limit cycles generating in a class of uncertain nonlinear systems which leads to stable oscillations in the system’s output.this is a wanted behavior in many practical engineering problems. for this purpose, first the equation of the desirable limit cycle is achieved according to shape, amplitude and frequency of the required output oscillations. then,...

Analysis of bifurcations of limit cycles with Lyapunov exponents and numerical normal forms

In this paper we focus on the combination of normal form and Lyapunov exponent computations in the numerical study of the three codim 2 bifurcations of limit cycles with dimension of the center manifold equal to 4 or to 5 in generic autonomous ODEs. The normal form formulas are independent of the dimension of the phase space and involve solutions of certain linear boundary-value problems. The f...

Unique Normal Forms for Nilpotent Planar Vector Fields

On Generating Small Clause Normal Forms

In this paper we focus on two powerful techniques to obtain compact clause normal forms: Renaming of formulae and reened Skolem-ization methods. We illustrate their eeect on various examples. By an exhaustive experiment of all rst-order TPTP problems, it shows that our clause normal form transformation yields fewer clauses and fewer literals than the methods known and used so far. This often al...