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Recent studies have demonstrated that a laser can self-generate frequency combs when tuned near an exceptional point (EP), where two cavity modes coalesce. These EP combs induce periodic modulation of the population inversion in the gain medium, and their repetition rate is independent of the laser cavity's free spectral range. In this work, we perform a stability analysis that reveals two notable properties of EP combs, bi-stability and a period-doubling cascade. The period-doubling cascade enables halving of the repetition rate while maintaining the comb's total bandwidth, presenting opportunities for the design of highly compact frequency comb generators.
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http://dx.doi.org/10.1515/nanoph-2025-0069 | DOI Listing |
Chaos
September 2025
Institute of Physics, University of São Paulo, 05508-900 São Paulo, SP, Brazil.
The memristor, theorized by Leon Chua in 1971, functions as a fundamental electronic component, directly linking electric charge and magnetic flux. As a result of their nonlinear characteristics, memristive circuits generally exhibit chaotic attractors in addition to periodicity. In this work, we consider the Muthuswamy-Chua system, a chaotic circuit consisting of an inductor, a capacitor, and a memristor.
View Article and Find Full Text PDFSci Rep
August 2025
Laboratory of Nonlinear Analysis and Applied Mathematics, Department of Mathematics, University of Tlemcen, 13000, Tlemcen, Algeria.
In the present article, a prey-predator-scavenger model is proposed and investigated with quadratic harvesting of predator and scavenger populations. The system is assumed to follow the Crowley-Martin functional response to describe the interaction between prey and predator populations. The positivity and boundedness of the system with respect to positive initial conditions are established.
View Article and Find Full Text PDFNanophotonics
June 2025
Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, 90089, USA.
Recent studies have demonstrated that a laser can self-generate frequency combs when tuned near an exceptional point (EP), where two cavity modes coalesce. These EP combs induce periodic modulation of the population inversion in the gain medium, and their repetition rate is independent of the laser cavity's free spectral range. In this work, we perform a stability analysis that reveals two notable properties of EP combs, bi-stability and a period-doubling cascade.
View Article and Find Full Text PDFChaos
February 2025
Departamento de Física, Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista (UNESP), 13506-900 Rio Claro, São Paulo, Brazil.
We consider the standard nontwist map with strong dissipation that leads the system to a 1D circular map with a quadratic sinusoidal oscillation and two control parameters. The 2D Lyapunov and isoperiodic diagrams reveal a complex interplay between domains of periodicity embedded in regions dominated by quasiperiodic and chaotic behaviors. Arnold tongues and shrimp-like, among other sets of periodicities, compose this rich dynamical scenario in the parameter space.
View Article and Find Full Text PDFJ Biol Phys
January 2025
Department of Mathematics, Vivekananda College, Thakurpukur, Kolkata, West Bengal, 700063, India.
A underlying complex dynamical behavior of double Allee effects in predator-prey system is studied in this article to understand the predator-prey relation more intensely from different aspects. We first propose a system with the Caputo sense fractional-order predator-prey system incorporating the Allee effect in prey populations to explain how the memory effect can change the different emergent states. Local stability analysis is analyzed by applying Matignon's condition for the FDE system.
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