Some techniques to show the existence and uniqueness of limit cycles, typically stated for smooth vector fields, are extended to continuous piecewise-linear differential systems. New results are obtained for systems with three linearity zones without symmetry and having one equilibrium point in the central region. We also revisit the case of systems with only two linear zones giving shorter pro...

The paper analyses the nature of limit cycles induced through the interaction of transformer tap changing and load dynamics. Linearization of a Poincaré map is used to prove local stability. An approximation is introduced which allows the map to be formulated explicitly. An estimate of the region of attraction can then be obtained.

The plate-dilution frequency technique described facilitates simultaneous enumeration of a wide range of physiologically different microorganisms in complex systems with a precision comparable to dilution tube (most probable number) methods. Replicate microsamples are inoculated from each member of a dilution series onto areas delineated on plates of prepoured solid media; the plates are incuba...

The space of functions A over the phase space of KdV-hierarchy is studied as a module over the ring D generated by commuting derivations. A D-free resolution of A is constructed by Babelon, Bernard and Smirnov by taking the classical limit of the construction in quantum integrable models assuming a certain conjecture. We propose another D-free resolution of A by extending the construction in th...

The aim of this paper is to introduce and study the notions of fuzzy upper $e$-limit set, fuzzy lower $e$-limit set and fuzzy $e$-continuously convergent functions. Properties and basic relationships among fuzzy upper $e$-limit set, fuzzy lower $e$- limit set and fuzzy $e$-continuity are investigated via fuzzy $e$-open sets.

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

abstract one of the methods for improving soil physical quality of arid and semiarid regions is the application of cheap organic conditioners such as sewage sludge. this research was conducted in large pots (50 cm diameter, 25 cm height) to study the effects of tabriz petrochemical biological sludge at 4 rates (25, 50, 75 and 100 tons/ha) on organic carbon (oc), mean weight diameter (mwd) of ag...

In this paper we classify the phase portraits in the Poincaré disc of the centers of the generalized class of Kukles systems ẋ = −y, ẏ = x+ axy + bxy, symmetric with respect to the y-axis, and we study, using the averaging theory up to sixth order, the limit cycles which bifurcate from the periodic solutions of these centers when we perturb them inside the class of all polynomial differential s...

We consider the class of polynomial differential equations ẋ = λx + Pn(x, y), ẏ = μy + Qn(x, y) in R where Pn(x, y) and Qn(x, y) are homogeneous polynomials of degree n > 1 and λ 6= μ, i.e. the class of polynomial differential systems with a linear node with different eigenvalues and homogeneous nonlinearities. For this class of polynomial differential equations we study the existence and non–e...

In this paper, we show that perturbing a simple 3-d quadratic system with a center-type singular point can yield at least 10 small-amplitude limit cycles around a singular point. This result improves the 7 limit cycles obtained recently in a simple 3-d quadratic system around a Hopf singular point. Compared with Bautin’s result for quadratic planar vector fields, which can only have 3 small-amp...