In:
International Journal of Bifurcation and Chaos, World Scientific Pub Co Pte Ltd, Vol. 33, No. 07 ( 2023-06-15)
Abstract:
For a class of three-dimensional piecewise linear systems with an admissible saddle-focus, the existence of three kinds of homoclinic loops is shown. Moreover, the birth and number of the periodic orbits induced by homoclinic bifurcation are investigated, and various sufficient conditions are obtained to guarantee the appearance of only one periodic orbit, finitely many periodic orbits or countably infinitely many periodic orbits. Furthermore, the stability of these newborn periodic orbits is analyzed in detail and some conclusions are made about them to be periodic saddle orbits or periodic sinks. Finally, some examples are given.
Type of Medium:
Online Resource
ISSN:
0218-1274
,
1793-6551
DOI:
10.1142/S0218127423500839
Language:
English
Publisher:
World Scientific Pub Co Pte Ltd
Publication Date:
2023
SSG:
11
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