Results 1 to 10 of about 333,140 (144)
Chemical Systems with Limit Cycles. [PDF]
Bull Math Biol, 2023 AbstractThe dynamics of a chemical reaction network (CRN) is often modeled under the assumption of mass action kinetics by a system of ordinary differential equations (ODEs) with polynomial right-hand sides that describe the time evolution of concentrations of chemical species involved. Given an arbitrarily large integer $$K \in {\mathbb N}$$
Erban R, Kang HW.
europepmc +6 more sources
Limit cycles and chaos in the hybrid atom-optomechanics system [PDF]
Scientific Reports, 2022 We consider atoms in two different periodic potentials induced by different lasers, one of which is coupled to a mechanical membrane via radiation pressure force.
Xingran Xu +2 more
doaj +2 more sources
Isochronous families of limit cycles
Electronic Journal of Differential Equations, 2018 In this article we present a method for determining if the frequency of a family of periodic orbits remains constant when a parameter changes. Two-dimensional systems of ordinary and delayed differential equations are considered.
Romina Cobiaga, Walter Reartes
doaj +3 more sources
The algebraic curves of planar polynomial differential systems with homogeneous nonlinearities
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We consider planar polynomial systems of ordinary differential equations of the form $\dot x = x + P_n(x,y)$, $\dot y = y + Q_n(x,y)$, where $P_n(x,y),\ Q_n(x,y)$ are homogeneous polynomials of degree $n$.
Vladimir Cheresiz, Evgenii Volokitin
doaj +1 more source
Pomeranchuk 100, 2014 In this review we consider the concept of limit cycles in the renormalization group flows. The examples of this phenomena in the quantum mechanics and field theory will be presented.
Bulycheva, K., Gorsky, A.
openaire +2 more sources
Rational limit cycles of Abel differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2023 We study the number of rational limit cycles of the Abel equation $x'=A(t)x^3+B(t)x^2$, where $A(t)$ and $B(t)$ are real trigonometric polynomials. We show that this number is at most the degree of $A(t)$ plus one.
José Luis Bravo +2 more
doaj +1 more source
Limit cycles in mass-conserving deficiency-one mass-action systems
Electronic Journal of Qualitative Theory of Differential Equations, 2022 We present some simple mass-action systems with limit cycles that fall under the scope of the Deficiency-One Theorem. All the constructed examples are mass-conserving and their stoichiometric subspace is two-dimensional.
Balázs Boros, Josef Hofbauer
doaj +1 more source
Rational Limit Cycles on Abel Polynomial Equations
Mathematics, 2020 In this paper we deal with Abel equations of the form d y / d x = A 1 ( x ) y + A 2 ( x ) y 2 + A 3 ( x ) y 3 , where A 1 ( x ) , A 2 ( x ) and A 3 ( x ) are real polynomials and A 3 ≢ 0 .
Claudia Valls
doaj +1 more source
Limit Cycles of Polynomially Integrable Piecewise Differential Systems
Axioms, 2023 In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides.
Belén García +3 more
doaj +1 more source
Limit Cycles of Lorenz System with Hopf Bifurcation [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2008 We prove that near the bifurcation point unstable limit cycle arises from the Lorenz system. In the analysis, we use the method of local bifurcation theory, especially the center manifold and the normal form theorem. A computer algebra system using Maple
Azad Amen, Rizgar Salih
doaj +1 more source