@article{mollik_kennedy_ul shougat_li_fitzgerald_echols_kirk_silverberg_perkins_2022, title={Discrete element method simulator for joint dynamics: a case study using a red-tailed hawk's hallux digit}, volume={6}, ISSN={["1573-272X"]}, DOI={10.1007/s11044-022-09828-x}, journal={MULTIBODY SYSTEM DYNAMICS}, author={Mollik, Tushar and Kennedy, Scott and Ul Shougat, Md Raf E. and Li, Xiaofu and Fitzgerald, Timothy and Echols, Scott and Kirk, Nick and Silverberg, Larry and Perkins, Edmon}, year={2022}, month={Jun} }
 @article{ul shougat_li_perkins_2022, title={Dynamic effects on reservoir computing with a Hopf oscillator}, volume={105}, ISSN={["2470-0053"]}, DOI={10.1103/PhysRevE.105.044212}, abstractNote={Limit cycle oscillators have the potential to be resourced as reservoir computers due to their rich dynamics. Here, a Hopf oscillator is used as a physical reservoir computer by discarding the delay line and time-multiplexing procedure. A parametric study is used to uncover computational limits imposed by the dynamics of the oscillator using parity and chaotic time-series prediction benchmark tasks. Resonance, frequency ratios from the Farey sequence, and Arnold tongues were found to strongly affect the computation ability of the reservoir. These results provide insights into fabricating physical reservoir computers from limit cycle systems.}, number={4}, journal={PHYSICAL REVIEW E}, author={Ul Shougat, Md Raf E. and Li, XiaoFu and Perkins, Edmon}, year={2022}, month={Apr} }
 @article{li_kallepalli_mollik_ul shougat_kennedy_frabitore_perkins_2022, title={The pendulum adaptive frequency oscillator}, volume={179}, ISSN={["1096-1216"]}, DOI={10.1016/j.ymssp.2022.109361}, abstractNote={Adaptive oscillators are a type of nonlinear oscillator that are capable of learning and storing information in plastic states. Here, a typical mechanical pendulum is modified to have an adjustable rod length to create a pendulum adaptive frequency oscillator. Since the resonance frequency of the pendulum is a function of the rod length, this allows the pendulum to learn and encode frequency information from an external source. An experimental pendulum adaptive frequency oscillator is designed and constructed, and its performance is compared to numerical simulations. This nonlinear pendulum was approximated as a Duffing oscillator through the method of multiple scales to determine the physical constants of the experiment by using a curve fit. Utilizing the pendulum adaptive frequency oscillator’s dynamics, this system is able to learn a resonance condition and store this information in the rod length. This causes the system to seek resonance, even with considerable nonlinearity. As pendulums can be used to harvest energy, this type of adaptation could be used to further exploit vibratory energy sources.}, journal={Mechanical Systems and Signal Processing}, author={Li, XiaoFu and Kallepalli, Pawan and Mollik, Tushar and Ul Shougat, Md Raf E and Kennedy, Scott and Frabitore, Sean and Perkins, Edmon}, year={2022}, month={Nov}, pages={109361} }
 @article{ul shougat_li_mollik_perkins_2021, title={A Hopf physical reservoir computer}, volume={11}, ISSN={["2045-2322"]}, DOI={10.1038/s41598-021-98982-x}, abstractNote={Abstract}, number={1}, journal={SCIENTIFIC REPORTS}, author={Ul Shougat, Md Raf E. and Li, XiaoFu and Mollik, Tushar and Perkins, Edmon}, year={2021}, month={Sep} }
 @article{li_ul shougat_kennedy_fendley_dean_beal_perkins_2021, title={A four-state adaptive Hopf oscillator}, volume={16}, ISSN={["1932-6203"]}, DOI={10.1371/journal.pone.0249131}, abstractNote={Adaptive oscillators (AOs) are nonlinear oscillators with plastic states that encode information. Here, an analog implementation of a four-state adaptive oscillator, including design, fabrication, and verification through hardware measurement, is presented. The result is an oscillator that can learn the frequency and amplitude of an external stimulus over a large range. Notably, the adaptive oscillator learns parameters of external stimuli through its ability to completely synchronize without using any pre- or post-processing methods. Previously, Hopf oscillators have been built as two-state (a regular Hopf oscillator) and three-state (a Hopf oscillator with adaptive frequency) systems via VLSI and FPGA designs. Building on these important implementations, a continuous-time, analog circuit implementation of a Hopf oscillator with adaptive frequency and amplitude is achieved. The hardware measurements and SPICE simulation show good agreement. To demonstrate some of its functionality, the circuit’s response to several complex waveforms, including the response of a square wave, a sawtooth wave, strain gauge data of an impact of a nonlinear beam, and audio data of a noisy microphone recording, are reported. By learning both the frequency and amplitude, this circuit could be used to enhance applications of AOs for robotic gait, clock oscillators, analog frequency analyzers, and energy harvesting.}, number={3}, journal={PLOS ONE}, author={Li, XiaoFu and Ul Shougat, Md Raf E. and Kennedy, Scott and Fendley, Casey and Dean, Robert N. and Beal, Aubrey N. and Perkins, Edmon}, year={2021}, month={Mar} }
 @article{ul shougat_li_mollik_perkins_2021, title={An Information Theoretic Study of a Duffing Oscillator Array Reservoir Computer}, volume={16}, ISSN={["1555-1415"]}, DOI={10.1115/1.4051270}, abstractNote={Abstract}, number={8}, journal={Journal of Computational and Nonlinear Dynamics}, author={Ul Shougat, Md. Raf E. and Li, XiaoFu and Mollik, Tushar and Perkins, Edmon}, year={2021}, month={Aug}, pages={081004} }
 @article{zhao_perkins_li_bond_marghitu_2021, title={Nonlinear vibratory properties of additive manufactured continuous carbon fiber reinforced polymer composites}, volume={117}, ISSN={["1433-3015"]}, DOI={10.1007/s00170-021-07456-x}, journal={The International Journal of Advanced Manufacturing Technology}, author={Zhao, Jing and Perkins, Edmon and Li, XiaoFu and Bond, Arthur and Marghitu, Dan}, year={2021}, pages={1077–1089} }
 @article{li_shougat_mollik_beal_dean_perkins_2021, title={Stochastic effects on a Hopf adaptive frequency oscillator}, volume={129}, ISSN={["1089-7550"]}, DOI={10.1063/5.0050819}, abstractNote={This paper explores the stochastic dynamics of a Hopf adaptive frequency oscillator when driven by noise. Adaptive oscillators are nonlinear oscillators that store information via plastic states. As noise is ubiquitous in physical systems, it is important to gain an understanding of the stochastic effects on adaptive oscillators. Previously, it has been shown that a simplified analysis of the Fokker–Planck equation results in affecting the plastic frequency state of these oscillators. However, when the full Fokker–Planck equation is considered, new behaviors are observed due to changes in oscillation amplitudes in addition to frequencies. The plastic frequency state of these oscillators may benefit from enhanced learning due to small amplitudes of noise, converge to incorrect values for medium amplitudes of noise, and even collapse to zero in the limit of large amplitudes of noise. Interestingly, not all averaged states collapse equally, which leads a two dimensional limit cycle to collapse into single dimensional oscillations when considering the averaged dynamics. These behaviors are compared analytically through the Fokker–Planck equation, numerically using the Euler–Maruyama simulations, and finally validated experimentally using an analog, electronic circuit. These results show that noise can enhance, mislead, or even reduce the dimensionality of the averaged adaptive Hopf oscillator.}, number={22}, journal={JOURNAL OF APPLIED PHYSICS}, author={Li, XiaoFu and Shougat, Md. Raf E. Ul and Mollik, Tushar and Beal, Aubrey N. and Dean, Robert N. and Perkins, Edmon}, year={2021}, month={Jun} }