Replicate periodic windows in the parameter space of driven oscillators |
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Authors: | ES Medeiros SLT de Souza RO Medrano-T IL Caldas |
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Institution: | aInstituto de Física, Universidade de São Paulo, São Paulo, Brazil;bUniversidade Federal de São João del-Rei, Campus Alto Paraopeba, Minas Gerais, Brazil;cDepartamento de Ciências Exatas e da Terra, Universidade Federal de São Paulo, Diadema, São Paulo, Brazil |
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Abstract: | In the bi-dimensional parameter space of driven oscillators, shrimp-shaped periodic windows are immersed in chaotic regions. For two of these oscillators, namely, Duffing and Josephson junction, we show that a weak harmonic perturbation replicates these periodic windows giving rise to parameter regions correspondent to periodic orbits. The new windows are composed of parameters whose periodic orbits have the same periodicity and pattern of stable and unstable periodic orbits already existent for the unperturbed oscillator. Moreover, these unstable periodic orbits are embedded in chaotic attractors in phase space regions where the new stable orbits are identified. Thus, the observed periodic window replication is an effective oscillator control process, once chaotic orbits are replaced by regular ones. |
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