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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

Experimental recordings of v1(t) (volts per ms) illustrating the successive complexification of antiperiodic wave patterns in the oscillator in Fig. 1, obtained when fixing L1 = 9.8 mH, L2 = 23.7 mH, R2 = 155 Ω, and increasing R1 = 2143 Ω (3 peaks), 2175 Ω (5 peaks), 2224 Ω (7 peaks), 2288 Ω (9 peaks), 2298 Ω (11 peaks), 2313 Ω (13 peaks).Note differences in time scales.
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f2: Experimental recordings of v1(t) (volts per ms) illustrating the successive complexification of antiperiodic wave patterns in the oscillator in Fig. 1, obtained when fixing L1 = 9.8 mH, L2 = 23.7 mH, R2 = 155 Ω, and increasing R1 = 2143 Ω (3 peaks), 2175 Ω (5 peaks), 2224 Ω (7 peaks), 2288 Ω (9 peaks), 2298 Ω (11 peaks), 2313 Ω (13 peaks).Note differences in time scales.

Mentions: Figure 2 presents typical experimental signals obtained for the voltage v1(t) on the capacitor C1 as a function of the resistance R1 while maintaining all other parameters constant. From this figure we recognize the characteristic signature of antiperiodic oscillations, namely where T/2 is the antiperiod and T is the period of the oscillation. From Fig. 2 it is easy to recognize that an antiperiodic function with antiperiod T is necessarily a periodic function with period 2T. Identical antiperiodicity is detected in measurements of v2, i1, or i2 (not shown). For all variables, we could follow the signal up to quite large number of spikes.


Antiperiodic oscillations.

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

Experimental recordings of v1(t) (volts per ms) illustrating the successive complexification of antiperiodic wave patterns in the oscillator in Fig. 1, obtained when fixing L1 = 9.8 mH, L2 = 23.7 mH, R2 = 155 Ω, and increasing R1 = 2143 Ω (3 peaks), 2175 Ω (5 peaks), 2224 Ω (7 peaks), 2288 Ω (9 peaks), 2298 Ω (11 peaks), 2313 Ω (13 peaks).Note differences in time scales.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: Experimental recordings of v1(t) (volts per ms) illustrating the successive complexification of antiperiodic wave patterns in the oscillator in Fig. 1, obtained when fixing L1 = 9.8 mH, L2 = 23.7 mH, R2 = 155 Ω, and increasing R1 = 2143 Ω (3 peaks), 2175 Ω (5 peaks), 2224 Ω (7 peaks), 2288 Ω (9 peaks), 2298 Ω (11 peaks), 2313 Ω (13 peaks).Note differences in time scales.
Mentions: Figure 2 presents typical experimental signals obtained for the voltage v1(t) on the capacitor C1 as a function of the resistance R1 while maintaining all other parameters constant. From this figure we recognize the characteristic signature of antiperiodic oscillations, namely where T/2 is the antiperiod and T is the period of the oscillation. From Fig. 2 it is easy to recognize that an antiperiodic function with antiperiod T is necessarily a periodic function with period 2T. Identical antiperiodicity is detected in measurements of v2, i1, or i2 (not shown). For all variables, we could follow the signal up to quite large number of spikes.

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