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Antiperiodic oscillations.

Freire JG, Cabeza C, Marti A, Pöschel T, Gallas JA - Sci Rep (2013)

Bottom Line: The investigation of regular and irregular patterns in nonlinear oscillators is an outstanding problem in physics and in all natural sciences.In general, regularity is understood as tantamount to periodicity.However, there is now a flurry of works proving the existence of "antiperiodicity", an unfamiliar type of regularity.

View Article: PubMed Central - PubMed

Affiliation: Institute for Multiscale Simulations, Friedrich-Alexander-Universität, Erlangen, Germany.

ABSTRACT
The investigation of regular and irregular patterns in nonlinear oscillators is an outstanding problem in physics and in all natural sciences. In general, regularity is understood as tantamount to periodicity. However, there is now a flurry of works proving the existence of "antiperiodicity", an unfamiliar type of regularity. Here we report the experimental observation and numerical corroboration of antiperiodic oscillations. In contrast to the isolated solutions presently known, we report infinite hierarchies of antiperiodic waveforms that can be tuned continuously and that form wide spiral-shaped stability phases in the control parameter plane. The waveform complexity increases towards the focal point common to all spirals, a key hub interconnecting them all.

No MeSH data available.


Related in: MedlinePlus

Schematic representation of the circuit used to measure the antiperiodic oscillations.This circuit is governed by the differential equations C1dv1/dt = i1 − iR(v1), C2dv2/dt = −i1 − i2 − iG(v2), L1di1/dt = v2 − v1 − i1R1, L2di2/dt = v2 − i2R2. The v-i characteristics of iR(v1) and iG(v2) are odd-symmetric functions given in the text.
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f1: Schematic representation of the circuit used to measure the antiperiodic oscillations.This circuit is governed by the differential equations C1dv1/dt = i1 − iR(v1), C2dv2/dt = −i1 − i2 − iG(v2), L1di1/dt = v2 − v1 − i1R1, L2di2/dt = v2 − i2R2. The v-i characteristics of iR(v1) and iG(v2) are odd-symmetric functions given in the text.

Mentions: Here, we report the experimental observation and numerical corroboration of apparently infinite sequences of such elusive antiperiodic oscillations in an autonomous electronic circuit (Fig. 1). Our key discovery is that the complexification of currents and voltages in the circuit occurs mediated by infinite families of self-sustained antiperiodic oscillations that can be tuned continuously as a function of the physical reactances involved. Nowadays, periodic waveforms are the rule in nonlinear systems while oscillators capable of supporting families of tunable antiperiodic waveforms with an unbounded number of peaks within an oscillation are completely unheard of. We detected tunable antiperiodicity while studying the complicated mechanisms underlying the progressive wave pattern complexification generated by the electronic circuit during period-doubling and period-adding cascades of bifurcations.


Antiperiodic oscillations.

Freire JG, Cabeza C, Marti A, Pöschel T, Gallas JA - Sci Rep (2013)

Schematic representation of the circuit used to measure the antiperiodic oscillations.This circuit is governed by the differential equations C1dv1/dt = i1 − iR(v1), C2dv2/dt = −i1 − i2 − iG(v2), L1di1/dt = v2 − v1 − i1R1, L2di2/dt = v2 − i2R2. The v-i characteristics of iR(v1) and iG(v2) are odd-symmetric functions given in the text.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3675356&req=5

f1: Schematic representation of the circuit used to measure the antiperiodic oscillations.This circuit is governed by the differential equations C1dv1/dt = i1 − iR(v1), C2dv2/dt = −i1 − i2 − iG(v2), L1di1/dt = v2 − v1 − i1R1, L2di2/dt = v2 − i2R2. The v-i characteristics of iR(v1) and iG(v2) are odd-symmetric functions given in the text.
Mentions: Here, we report the experimental observation and numerical corroboration of apparently infinite sequences of such elusive antiperiodic oscillations in an autonomous electronic circuit (Fig. 1). Our key discovery is that the complexification of currents and voltages in the circuit occurs mediated by infinite families of self-sustained antiperiodic oscillations that can be tuned continuously as a function of the physical reactances involved. Nowadays, periodic waveforms are the rule in nonlinear systems while oscillators capable of supporting families of tunable antiperiodic waveforms with an unbounded number of peaks within an oscillation are completely unheard of. We detected tunable antiperiodicity while studying the complicated mechanisms underlying the progressive wave pattern complexification generated by the electronic circuit during period-doubling and period-adding cascades of bifurcations.

Bottom Line: The investigation of regular and irregular patterns in nonlinear oscillators is an outstanding problem in physics and in all natural sciences.In general, regularity is understood as tantamount to periodicity.However, there is now a flurry of works proving the existence of "antiperiodicity", an unfamiliar type of regularity.

View Article: PubMed Central - PubMed

Affiliation: Institute for Multiscale Simulations, Friedrich-Alexander-Universität, Erlangen, Germany.

ABSTRACT
The investigation of regular and irregular patterns in nonlinear oscillators is an outstanding problem in physics and in all natural sciences. In general, regularity is understood as tantamount to periodicity. However, there is now a flurry of works proving the existence of "antiperiodicity", an unfamiliar type of regularity. Here we report the experimental observation and numerical corroboration of antiperiodic oscillations. In contrast to the isolated solutions presently known, we report infinite hierarchies of antiperiodic waveforms that can be tuned continuously and that form wide spiral-shaped stability phases in the control parameter plane. The waveform complexity increases towards the focal point common to all spirals, a key hub interconnecting them all.

No MeSH data available.


Related in: MedlinePlus