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 focuses on investigating the bifurcation of limit cycles and centers within a specific class three-dimensional cubic systems possessing Z3-equivariant symmetry. By calculating singular point values systems, we obtain necessary condition for to be center. Subsequently, Darboux integral method is employed demonstrate that this also sufficient. Additionally, system can bifurcate 15 smal...

We solve the center-focus problem in a class of piecewise quadratic polynomial differential systems with an invariant straight line. The separation curve is also line which not invariant. provide families having at origin weak-foci maximal order. In continuous class, cyclicity solved, being 3 such number. Moreover, for discontinuous but without sliding segment, we prove existence 7 limit cycles...

Reaction delays play an important role in determining the qualitative dynamical properties of a platoon of vehicles driving on a straight road. In this paper, we investigate the impact of delayed feedback on the dynamics of a recently-proposed car-following model; namely, the Reduced Classical Car-Following Model (RCCFM). Specifically, we analyse the RCCFM in three regimes – no delay, small del...

Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical behavior. While tipping in a fold bifurcation of an equilibrium is well understood, much less is known about tipping of oscillations (limit cycles) though this d...

Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the system's parameters abruptly shift the system to an alternative state with a contrasting dynamical behavior. While tipping in a fold bifurcation of an equilibrium is well understood, much less is known about tipping of oscillations (limit cycles) though this ...

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...

we consider the number of zeros of the integral $i(h) = oint_{gamma_h} omega$ of real polynomial form $omega$ of degree not greater than $n$ over a family of vanishing cycles on curves $gamma_h:$ $y^2+3x^2-x^6=h$, where the integral is considered as a function of the parameter $h$. we prove that the number of zeros of $i(h)$, for $0 < h < 2$, is bounded above by $2[frac{n-1}{2}]+1$.