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On Physically Unacceptable Numerical Solutions Yielding Strong Chaotic Signals.
1Department of Computer Science, Opole University of Technology, 45-758 Opole, Poland.
Entropy (Basel, Switzerland)
|June 24, 2022
Summary
Unphysical numerical solutions from nonlinear circuit simulations can generate useful chaotic sequences. These chaotic sequences, derived from unacceptable numerical results, show potential for cryptography and secure data transmission.
Area of Science:
- Nonlinear dynamics and circuits
- Computational mathematics
- Chaos theory
Background:
- Numerical solutions for nonlinear systems can yield physically unacceptable results.
- The choice of numerical solvers is critical for accurate system analysis.
- Memristive circuits present unique challenges in numerical simulation.
Purpose of the Study:
- To analyze physically unacceptable numerical solutions in nonlinear circuits.
- To investigate the potential of these unphysical solutions as sources of chaos.
- To explore applications of chaotic sequences derived from numerical artifacts.
Main Methods:
- Analysis of a nonlinear memristive circuit using an ill-designed numerical approach.
- Verification of unphysical trajectories violating system invariants.
- Application of the 0-1 test for chaos and bifurcation diagrams.
Main Results:
- An ill-designed numerical method produced unphysical, unacceptable trajectories for a memristive circuit.
- These unacceptable numerical solutions were demonstrated to be strong chaotic sequences.
- The 0-1 test and bifurcation diagrams confirmed the chaotic nature of the numerical output.
Conclusions:
- Physically unacceptable numerical solutions can be repurposed as valuable chaotic sequences.
- These chaotic sequences have potential applications in cryptography and secure data transmission.
- The study highlights the dual nature of numerical errors: a source of inaccuracy and a generator of useful chaos.
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