S-systems are simple examples of power-law dynamical systems (polynomial systems with real exponents). For planar S-systems, we study global stability of the unique positive equilibrium and solve the center problem. Further, we construct a planar S-system with two limit cycles.

We consider the time-dependent non linear Schrödinger equations with a double well potential in dimensions d = 1 and d = 2. We prove, in the semiclassical limit, that the finite dimensional eigenspace associated to the lowest two eigenvalues of the linear operator is almost invariant for any time.

This paper deals with the problem of finding upper bounds on the number of periodic solutions of a class of one-dimensional non-autonomous differential equations: those with the right-hand sides being polynomials of degree n and whose coefficients are real smooth 1-periodic functions. The case n = 3 gives the so-called Abel equations which have been thoroughly studied and are quite understood. ...

This paper presents a procedure to find all limit sets near bifurcating equilibria in continuous, piecewise affine systems defined on a conic partition of R. To guarantee completeness of the obtained limit sets, new conditions for the existence or absence of limit cycles are combined with the study of return maps. With these results a complete bifurcation analysis of a class of planar conewise ...

This paper investigates the efficiency of a 2-period gait from the kinetic energy view-point. First, we formulate a steady 2-period gait for a compass-like bipedal robot by using a simple recurrence formula for the kinetic energy of an asymmetric rimless wheel. Second, we theoretically show that, in the case that the mean value of the hip angle is constant, the generated 2-period steady gait is...

Limit points for the positive eigenvalues of the normalized Laplacian matrix of a graph are considered. Specifically, it is shown that the set of limit points for the j-th smallest such eigenvalues is equal to [0, 1], while the set of limit points for the j-th largest such eigenvalues is equal to [1, 2]. Limit points for certain functions of the eigenvalues, motivated by considerations for rand...

In this paper we study those cubic systems which are invariant under a rotation of 2π/4 radians. They are written as ż = εz + p z2z̄ − z̄3, where z is complex, the time is real, and ε = ε1+ iε2, p = p1+ ip2 are complex parameters. When they have some critical points at infinity, i.e. |p2| ≤ 1, it is well-known that they can have at most one (hyperbolic) limit cycle which surrounds the origin. On ...

This note shows, by means of two simple, three-strategy games, the existence of stable periodic orbits and of multiple, interior steady states in a smooth version of the Best Response Dynamics, the Logit Dynamics. The main finding is that, unlike Replicator Dynamics, generic Hopf bifurcation and thus, stable limit cycles, occur under the Logit Dynamics, even for three strategy games. We also sh...

The use of delayed feedback of position for the control of oscillatory behaviour is analysed. It is shown that linear feedback can annihilate limit cycles and stabilize the origin. Furthermore, it is possible to create an asymptotically stable limit cycle with any prescribed amplitude using a simple nonlinear feedback. For almost all values of the delay, these feats can be achieved without usin...

For a given family of planar differential equations it is a very difficult problem to determine an upper bound for the number of its limit cycles. Even when this upper bound is one it is not always an easy problem to distinguish between the case of zero and one limit cycle. This note mainly deals with this second problem for a family of systems with a homogeneous nonlinear part. While the condi...