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Radiophysical model of the Rossler system using RC-filters
The purpose of the study is to develop and experimentally implement a radiophysical analog model of the Rossler system based on first-order low-pass RC filters, allowing for a reduction in the number of active elements in the circuit.
Methods. The original system of Rossler differential equations was adapted for experimental implementation: scaling of the dynamic variables was introduced to bring the voltages within the operating range of the operational amplifiers and analog multiplier. Three first-order rc filters were used instead of classical operational amplifier integrators. Based on this, a schematic diagram was developed that includes only two operational amplifiers and one analog multiplier. The experimental study was performed using a digital
oscilloscope; time series were recorded and phase portraits were constructed for various values of the control parameter.
Results: An experimental model of the Rossler system was created, containing only two operational amplifiers and one analog multiplier. When varying the control parameter in the developed circuit, a cascade of period-doubling bifurcations was observed. Phase portraits of period cycles of 1, 2, and 4 and the chaotic attractor were constructed based on experimental implementations. The resulting phase portraits qualitatively correspond to those obtained in numerical simulations of the R¨ossler system with traditionally used control
parameter values. The feasibility of the proposed approach and the possibility of observing the chaotic attractor are confirmed.
Conclusion: A new approach to analog modeling of the Rossler system is proposed and experimentally implemented. This approach utilizes first-order RC filters instead of classical operational amplifier integrators. This approach simplifies the circuit design while preserving the fundamental properties of the simulated system. The developed model opens up prospects for creating simple, inexpensive, and technologically advanced devices for demonstrating chaotic regimes, which is especially important for educational laboratories and research tasks requiring visual physical modeling of nonlinear dynamic systems. The obtained results are of particular importance for the study of the collective dynamics of networks of interacting oscillators in a radiophysical experiment, for which simplification of the design of the nodal element is critically important.
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