Asymptotics of Multiple Orthogonal Hermite Polynomials $$H_{n_1,n_2}(z,\alpha)$$ Determined by a Third-Order Differential Equation

2021 ◽  
Vol 28 (4) ◽  
pp. 439-454
Author(s):  
S. Yu. Dobrokhotov ◽  
A. V. Tsvetkova
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Hermite Polynomials ◽  
Third Order ◽  
Third Order Differential Equation

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

Chaotic attractors based on unstable dissipative systems via third-order differential equation

2016 ◽  
Vol 27 (01) ◽  
pp. 1650008 ◽  
Author(s):  
E. Campos-Cantón
Keyword(s):  
Differential Equation ◽  
Equilibrium Point ◽  
Order Differential Equation ◽  
Dissipative System ◽  
Switching Control ◽  
Dissipative Systems ◽  
Control Law ◽  
Third Order ◽  
Third Order Differential Equation ◽  
2D And 3D

In this paper, we present an approach how to yield 1D, 2D and 3D-grid multi-scroll chaotic systems in [Formula: see text] based on unstable dissipative systems via third-order differential equation. This class of systems is constructed by a switching control law(SCL) changing the equilibrium point of an unstable dissipative system. The switching control law that governs the position of the equilibrium point varies according to the number of scrolls displayed in the attractor.

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