On central dispersions of the differential equation Y″=q(t)Y with periodic coefficients

1974 ◽  
pp. 47-61 ◽  
Author(s):  
O. Boruvka
Keyword(s):  
Differential Equation ◽  
Periodic Coefficients

scholarly journals Parametric Excitation and Evolutionary Dynamics

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
Rocio E. Ruelas ◽  
David G. Rand ◽  
Richard H. Rand
Keyword(s):  
Differential Equation ◽  
Parametric Excitation ◽  
Variable Coefficient ◽  
Evolutionary Dynamics ◽  
Replicator Equation ◽  
Periodic Coefficients ◽  
Forcing Function ◽  
Governing Differential Equation ◽  
Social Applications ◽  
Dynamics Problems

Parametric excitation refers to dynamics problems in which the forcing function enters into the governing differential equation as a variable coefficient. Evolutionary dynamics refers to a mathematical model of natural selection (the “replicator” equation) which involves a combination of game theory and differential equations. In this paper we apply perturbation theory to investigate parametric resonance in a replicator equation having periodic coefficients. In particular, we study evolution in the Rock-Paper-Scissors game, which has biological and social applications. Here periodic coefficients could represent seasonal variation. We show that 2:1 subharmonic resonance can destabilize the usual “Rock-Paper-Scissors” equilibrium for parameters located in a resonant tongue in parameter space. However, we also show that the tongue may be absent or very small if the forcing parameters are chosen appropriately.

Periodic solutions of a linear differential equation of the second order with periodic coefficients

1926 ◽  
Vol 23 (1) ◽  
pp. 44-46 ◽  
Author(s):  
E. L. Ince
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Periodic Solutions ◽  
Second Order ◽  
Hill’S Equation ◽  
Periodic Coefficients ◽  
Hill's Equation ◽  
Linear Differential ◽  
Image Position

The equation to be considered is of the typewhere p (x) is continuous for all real values of x, even, and periodic. It is no restriction to suppose that the period is π, and this assumption will be made, so that the equation is virtually Hill's equation.

scholarly journals Critical Oscillation Constant for Euler Type Half-Linear Differential Equation Having Multi-Different Periodic Coefficients

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Adil Misir ◽  
Banu Mermerkaya
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Order Differential Equation ◽  
Second Order ◽  
Periodic Coefficients ◽  
Second Order Differential Equation ◽  
Linear Differential ◽  
Critical Oscillation ◽  
Oscillation Constant

We compute explicitly the oscillation constant for Euler type half-linear second-order differential equation having multi-different periodic coefficients.

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