Asymptotical Formulas For Solutions Of Linear Differential Systems Of The First Order

1999 ◽  
Vol 36 (3-4) ◽  
pp. 342-353 ◽  
Author(s):  
Viktor S. Rykhlov
Keyword(s):  
Differential Systems ◽  
First Order ◽  
Linear Differential Systems ◽  
Linear Differential

scholarly journals ON THE NUMBER OF LIMIT CYCLES FOR DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS IN ℝ2n WITH TWO ZONES

2013 ◽  
Vol 23 (02) ◽  
pp. 1350024 ◽  
Author(s):  
JAUME LLIBRE ◽  
FENG RONG
Keyword(s):  
Small Parameter ◽  
Limit Cycles ◽  
Piecewise Linear ◽  
Displacement Function ◽  
Averaging Theory ◽  
Differential Systems ◽  
First Order ◽  
Linear Differential Systems ◽  
Order Expansion ◽  
Linear Differential

We study the number of limit cycles of the discontinuous piecewise linear differential systems in ℝ2n with two zones separated by a hyperplane. Our main result shows that at most (8n - 6)n-1 limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small parameter. For proving this result, we use the averaging theory in a form where the differentiability of the system is not necessary.

scholarly journals LIMIT CYCLES OF DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS

2011 ◽  
Vol 21 (11) ◽  
pp. 3181-3194 ◽  
Author(s):  
PEDRO TONIOL CARDIN ◽  
TIAGO DE CARVALHO ◽  
JAUME LLIBRE
Keyword(s):  
Limit Cycles ◽  
Piecewise Linear ◽  
Displacement Function ◽  
Two Dimensional ◽  
Bifurcation Of Limit Cycles ◽  
Differential Systems ◽  
First Order ◽  
Linear Differential Systems ◽  
Order Expansion ◽  
Linear Differential

We study the bifurcation of limit cycles from the periodic orbits of a two-dimensional (resp. four-dimensional) linear center in ℝn perturbed inside a class of discontinuous piecewise linear differential systems. Our main result shows that at most 1 (resp. 3) limit cycle can bifurcate up to first-order expansion of the displacement function with respect to the small parameter. This upper bound is reached. For proving these results, we use the averaging theory in a form where the differentiability of the system is not needed.

Generalized systems of linear differential equations

1981 ◽  
Vol 89 (1-2) ◽  
pp. 1-14 ◽  
Author(s):  
Rainer Pfaff
Keyword(s):  
Differential Equations ◽  
Bounded Variation ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Differential Systems ◽  
First Order ◽  
Linear Differential Systems ◽  
Generalized Systems ◽  
Linear Differential ◽  
Derivatives Of

SynopsisWe consider ordinary linear differential systems of first order with distributional coefficients and distributional nonhomogeneous terms. Firstly the coefficients are assumed to be functions, secondly to be first order distributions (i.e. first derivatives of functions which are integrable or of bounded variation), and thirdly to be distributions of higher order.

scholarly journals Differential Transcendency in the Theory of Linear Differential Systems with Constant Coefficients

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
Branko Malešević ◽  
Dragana Todorić ◽  
Ivana Jovović ◽  
Sonja Telebaković
Keyword(s):  
Cauchy Problem ◽  
Linear System ◽  
Order Operator ◽  
Operator Equations ◽  
Differential Systems ◽  
First Order ◽  
Linear Differential Systems ◽  
Constant Coefficients ◽  
Linear Differential

We consider a reduction of a nonhomogeneous linear system of first-order operator equations to a totally reduced system. Obtained results are applied to Cauchy problem for linear differential systems with constant coefficients and to the question of differential transcendency.

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