The bifurcation of limit cycles in single-input single-output control systems with saturation is considered. Under some non-degeneracy conditions, a theorem characterizing such bifurcation is stated for the cases of dimension two and three. In terms of the deviation from the critical value of the bifurcation parameter, expressions in form of power series for the period, amplitude and the charac...

In this paper, stability and bifurcation of piecewise affine systems is investigated. In the stability analysis, stability of the origin and existence of limit cycles are investigated by means of the radial growth rate, which describes the behavior of the radial direction of the trajectories. In the bifurcation analysis, Hopf bifurcation and saddle-node bifurcation is discussed. The radial grow...

This paper presents an analysis on the bifurcation of limit cycles for a cubic Hamiltonian system with quintic perturbed terms using both qualitative analysis and numerical exploration. The perturbed terms considered here is in the form of R(x, y, λ) = S(x, y, λ) = mx+ny+kxy−λ, where m, n, k, and λ are all variable. The investigation is based on detection functions which are particularly effect...

Theoretical results regarding two-dimensional ordinary-differential equations (ODEs) with second-degree polynomial right-hand sides are summarized, with a focus on multistability, limit cycles and limit cycle bifurcations. The results are then used for construction of two reaction systems, which are at the deterministic level described by twodimensional third-degree kinetic ODEs. The first syst...

We consider a predator-prey system with nonmonotonic functional response: p(x) = mx ax2+bx+1 . By allowing b to be negative (b > −2 √ a), p(x) is concave up for small values of x > 0 as it is for the sigmoidal functional response. We show that in this case there exists a Bogdanov–Takens bifurcation point of codimension 3, which acts as an organizing center for the system. We study the Hopf and ...

We study the effect of a time-delayed feedback within a generic model for a saddle-node bifurcation on a limit cycle. Without delay the only attractor below this global bifurcation is a stable node. Delay renders the phase space infinite-dimensional and creates multistability of periodic orbits and the fixed point. Homoclinic bifurcations, period-doubling and saddle-node bifurcations of limit c...

In this paper friction induced limit cycles are predicted for a simple motion system of a single motor-driven inertia subjected to friction and a PID-controlled regulator task. The two friction models used, i.e., (i) the dynamic LuGre friction model and (ii) the static Switch friction model, are compared with respect to the so-called hunting phenomenon. Analysis tools originating from the field...

In this paper friction induced limit cycles are predicted for a simple motion system of a single motor-driven inertia subjected to friction and a PID-controlled regulator task. The two friction models used, i.e., (i) the dynamic LuGre friction model and (ii) the static Switch friction model, are compared with respect to the so-called hunting phenomenon. Analysis tools originating from the field...