Periodic solutions of systems of differential equations with random right-hand sides

1997 ◽  
Vol 49 (2) ◽  
pp. 247-252
Author(s):  
D. I. Martynyuk ◽  
V. Ya. Danilov ◽  
A. N. Stanzhitskii
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Systems Of Differential Equations ◽  
Right Hand

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.

scholarly journals On the periodic solutions of linear homogenous systems of differential equations

1982 ◽  
Vol 5 (2) ◽  
pp. 305-309
Author(s):  
A. K. Bose
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Fundamental Matrix ◽  
Solution Space ◽  
Order System ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Scalar Matrix ◽  
Systems Of Differential Equations ◽  
Necessary And Sufficient

Given a fundamental matrixϕ(x)of ann-th order system of linear homogeneous differential equationsY′=A(x)Y, a necessary and sufficient condition for the existence of ak-dimensional(k≤n)periodic sub-space (of periodT) of the solution space of the above system is obtained in terms of the rank of the scalar matrixϕ(t)−ϕ(0).

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