scholarly journals PERIODIC SOLUTIONS OF SYSTEMS OF AUTONOMOUS DIFFERENTIAL EQUATIONS WITH VARIABLE STRUCTURE AND IMPULSES

2015 ◽  
Vol 105 (4) ◽  
Author(s):  
K.G. Dishlieva
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Variable Structure ◽  
Autonomous Differential Equations

scholarly journals PERIODIC SOLUTIONS OF A MODEL OF LOTKA-VOLTERRA WITH VARIABLE STRUCTURE AND IMPULSES

2015 ◽  
Vol 11 (6) ◽  
pp. 5317-5325
Author(s):  
Katya Dishlieva ◽  
Katya Dishlieva
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Variable Structure ◽  
Impulsive Effects ◽  
Volterra Model ◽  
Right Hand

We consider a generalized version of the classical Lotka Volterra model with differential equations. The version has a variable structure (discontinuous right hand side) and the solutions are subjected to the discrete impulsive effects. The moments of right hand side discontinuity and the moments of impulsive effects coincide and they are specific for each solution. Using the Brouwer fixed point theorem, sufficient conditions for the existence of periodic solution are found.

Non-autonomous equations related to polynomial two-dimensional systems

1987 ◽  
Vol 105 (1) ◽  
pp. 129-152 ◽  
Author(s):  
M. A. M. Alwash ◽  
N. G. Lloyd
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
One Dimensional ◽  
Introductory Section ◽  
Independent Variable ◽  
Autonomous Differential Equations

SynopsisPeriodic solutions of certain one-dimensional non-autonomous differential equations are investigated (equation (1.4)); the independent variable is complex. The motivation, which is explained in the introductory section, is the connection with certain polynomial two-dimensional systems. Several classes of coefficients are considered; in each case the aim is to estimate the maximum number of periodic solutions into which a given solution can bifurcate under perturbation of the coefficients. In particular, we need to know when there is a full neighbourhood of periodic solutions. We give a number of sufficient conditions and investigate the implications for the corresponding two-dimensional systems.

Periodic solutions of polynomial non-autonomous differential equations

1993 ◽  
Vol 123 (5) ◽  
pp. 783-801 ◽  
Author(s):  
J. Devlin
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Periodic Functions ◽  
Autonomous Differential Equations ◽  
Image Position ◽  
The Way

Let ℐN denote the set of (N + 1)-tuples of C1 ω-periodic functions; the point P = (pN,…, p1p0) ϵ ℐN is identified with the differential equationWe examine the way in which the total number of ω-periodic solutions can vary as P traverses a path in ℐN.

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