Uniqueness and Non-uniqueness of Limit Cycles for Piecewise Linear Differential Systems with Three Zones and No Symmetry
Some techniques for proving the existence and uniqueness of limit cycles for smooth differential systems are extended to continuous piecewise linear differential systems with two and three zones and no symmetry. For planar systems with three linearity zones, the existence of two limit cycles surroun...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2015 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:145353 |
| Online Access: | https://ddd.uab.cat/record/145353 https://dx.doi.org/urn:doi:10.1007/s00332-015-9244-y |
| Access Level: | Open access |
| Keyword: | Liénard piecewise linear differential systems Limit cycles Nonlinear control systems Periodic orbit |
| Summary: | Some techniques for proving the existence and uniqueness of limit cycles for smooth differential systems are extended to continuous piecewise linear differential systems with two and three zones and no symmetry. For planar systems with three linearity zones, the existence of two limit cycles surrounding the only equilibrium point at the origin is rigorously shown for the first time. The usefulness of the achieved analytical results is illustrated by considering non-symmetric memristor-based electronic oscillators. |
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