Conditions for approaching the origin without intersecting the x-axis in the liénard plane

Asadollah Aghajani; Mohsen Mirafzal; Donald O’Regan

doi:10.2298/FIL1712761A

Conditions for approaching the origin without intersecting the x-axis in the liénard plane

Asadollah Aghajani, Mohsen Mirafzal, Donald O’Regan

Mathematics

Iran University of Science and Technology

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

Abstract

We consider the Liénard system in the plane and present general assumptions to obtain some new explicit conditions under which this system has or fails to have a positive orbit which starts at a point on the vertical isocline and approaches the origin without intersecting the x-axis. This arises naturally in the existence of homoclinic orbits and oscillatory solutions. Our investigation is based on the notion of orthogonal trajectories of orbits of the system.

Original language	English
Pages (from-to)	3761-3770
Number of pages	10
Journal	Filomat
Volume	31
Issue number	12
DOIs	https://doi.org/10.2298/FIL1712761A
Publication status	Published - 2017

Keywords

Homoclinic orbit
Limit cycle
Liénard system
Oscillation

Access to Document

10.2298/FIL1712761A

Cite this

@article{bc29b2e0386647008ed4968f7aab6340,

title = "Conditions for approaching the origin without intersecting the x-axis in the li{\'e}nard plane",

abstract = "We consider the Li{\'e}nard system in the plane and present general assumptions to obtain some new explicit conditions under which this system has or fails to have a positive orbit which starts at a point on the vertical isocline and approaches the origin without intersecting the x-axis. This arises naturally in the existence of homoclinic orbits and oscillatory solutions. Our investigation is based on the notion of orthogonal trajectories of orbits of the system.",

keywords = "Homoclinic orbit, Limit cycle, Li{\'e}nard system, Oscillation",

author = "Asadollah Aghajani and Mohsen Mirafzal and Donald O{\textquoteright}Regan",

year = "2017",

doi = "10.2298/FIL1712761A",

language = "English",

volume = "31",

pages = "3761--3770",

journal = "Filomat",

issn = "0354-5180",

publisher = "Universitet of Nis",

number = "12",

}

TY - JOUR

T1 - Conditions for approaching the origin without intersecting the x-axis in the liénard plane

AU - Aghajani, Asadollah

AU - Mirafzal, Mohsen

AU - O’Regan, Donald

PY - 2017

Y1 - 2017

N2 - We consider the Liénard system in the plane and present general assumptions to obtain some new explicit conditions under which this system has or fails to have a positive orbit which starts at a point on the vertical isocline and approaches the origin without intersecting the x-axis. This arises naturally in the existence of homoclinic orbits and oscillatory solutions. Our investigation is based on the notion of orthogonal trajectories of orbits of the system.

AB - We consider the Liénard system in the plane and present general assumptions to obtain some new explicit conditions under which this system has or fails to have a positive orbit which starts at a point on the vertical isocline and approaches the origin without intersecting the x-axis. This arises naturally in the existence of homoclinic orbits and oscillatory solutions. Our investigation is based on the notion of orthogonal trajectories of orbits of the system.

KW - Homoclinic orbit

KW - Limit cycle

KW - Liénard system

KW - Oscillation

UR - https://www.scopus.com/pages/publications/85029925414

U2 - 10.2298/FIL1712761A

DO - 10.2298/FIL1712761A

M3 - Article

SN - 0354-5180

VL - 31

SP - 3761

EP - 3770

JO - Filomat

JF - Filomat

IS - 12

ER -

Conditions for approaching the origin without intersecting the x-axis in the liénard plane

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this