In the field of economic growth, a huge interest has been devoted to explain the mechanisms through which a nonlinear system looses its stability and starts to oscillate around the steady state. Since the seminal Kalekian analysis, limit cycles represent the theoretical way of characterizing the emergence of persistent oscillations of macro-economic variables, namely the rise of indeterminacy p...

In this paper, we show how to analyze bifurcation and limit cycles for biological systems by using an algebraic approach based on triangular decomposition, Gröbner bases, discriminant varieties, real solution classification, and quantifier elimination by partial CAD. The analysis of bifurcation and limit cycles for a concrete two-dimensional system, the self-assembling micelle system with chemi...

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 $2[frac{n-1}{2}]+1$.

Physical limits place bounds on the divergent behaviour of dynamical systems. The paper explores this situation, providing an example where generator field-voltage limits capture behaviour, giving rise to a stable, though non-smooth, limit cycle. It is shown that shooting methods can be adapted to solve for such non-smooth switching-induced limit cycles. By continuing branches of switching-indu...

in this paper, we introduce fractional order of a planar fractional prey-predator system with a nonmonotonic functional response and anti-predator behaviour such that the adult preys can attack vulnerable predators. we analyze the existence and stability of all possibleequilibria. numerical simulations reveal that anti-predator behaviour notonly makes the coexistence of the prey and predator po...

Two-dimensional polynomial dynamical systems are mainly considered. We develop Erugin’s two-isocline method for the global analysis of such systems, construct canonical systems with field-rotation parameters and study various limit cycle bifurcations. In particular, we show how to carry out the classification of separatrix cycles and consider the most complicated limit cycle bifurcation: the bi...