scholarly journals Evolution of specialization in a plant‐microbial mutualism is explained by the oscillation theory of speciation

Evolution ◽  
2021 ◽  
Author(s):  
L. Torres‐Martínez ◽  
S. S Porter ◽  
C. E Wendlandt ◽  
J. Purcell ◽  
G.S. Ortiz‐Barbosa ◽  
...  
Keyword(s):  
Oscillation Theory ◽  
Evolution Of Specialization

Amplitude, phase, frequency—fundamental concepts of oscillation theory

1977 ◽  
Vol 123 (12) ◽  
pp. 657 ◽  
Author(s):  
D.E. Vakman ◽  
L.A. Vainshtein
Keyword(s):  
Oscillation Theory

scholarly journals Second-order impulsive differential systems with mixed and several delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shyam Sundar Santra ◽  
Apurba Ghosh ◽  
Omar Bazighifan ◽  
Khaled Mohamed Khedher ◽  
Taher A. Nofal
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Oscillation Theory ◽  
Second Order ◽  
Neutral Delay ◽  
Differential Systems ◽  
Impulsive Differential Systems ◽  
Several Delays ◽  
Necessary And Sufficient

AbstractIn this work, we present new necessary and sufficient conditions for the oscillation of a class of second-order neutral delay impulsive differential equations. Our oscillation results complement, simplify and improve recent results on oscillation theory of this type of nonlinear neutral impulsive differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

scholarly journals Dynamic behaviors of a nonautonomous predator–prey system with Holling type II schemes and a prey refuge

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yumin Wu ◽  
Fengde Chen ◽  
Caifeng Du
Keyword(s):  
Lyapunov Function ◽  
Differential Equations ◽  
Comparison Theorem ◽  
Sufficient Conditions ◽  
Oscillation Theory ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System

AbstractIn this paper, we consider a nonautonomous predator–prey model with Holling type II schemes and a prey refuge. By applying the comparison theorem of differential equations and constructing a suitable Lyapunov function, sufficient conditions that guarantee the permanence and global stability of the system are obtained. By applying the oscillation theory and the comparison theorem of differential equations, a set of sufficient conditions that guarantee the extinction of the predator of the system is obtained.

scholarly journals Renormalized oscillation theory for Hamiltonian systems

2017 ◽  
Vol 311 ◽  
pp. 569-597 ◽  
Author(s):  
Fritz Gesztesy ◽  
Maxim Zinchenko
Keyword(s):  
Hamiltonian Systems ◽  
Oscillation Theory

Oscillation Theory

1994 ◽  
pp. 275-305
Author(s):  
V. Lakshmikantham ◽  
Lizhi Wen ◽  
Binggen Zhang
Keyword(s):  
Oscillation Theory
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