We study a multimode semiconductor laser subject to a moderate optical feedback. The steady state is destabilized by either a simple Hopf bifurcation leading to in phase dynamics or by a degenerate Hopf bifurcation leading to antiphase dynamics. The degenerate bifurcation is also a source of multiple coexisting attractors. We show that a simple interpretation of the low frequency fluctuations in the multimode regime is provided by a chaotic itinerancy among the many coexisting unstable attractors produced by the degenerate Hopf bifurcation.
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http://dx.doi.org/10.1103/PhysRevLett.85.3157 | DOI Listing |
Infect Dis Model
June 2025
School of Mathematical Sciences, Universiti Sains Malaysia, 11700, Glugor, Pulau Penang, Malaysia.
Hybrid-immune and immunodeficient individuals have been identified by the World Health Organization as two vulnerable groups in the context of COVID-19, but their distinct characteristics remain underexplored. To address this gap, we developed an extended compartmental model that simulates the spread of COVID-19 and the impact of administering three doses of the vaccine (first, second, and booster). This study aims to provide insights into how these vulnerable populations respond to vaccination and the dynamics of waning immunity.
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January 2025
Department of Biology, Faculty of Science, Kyushu University, 744 Motooka, Nishi-Ku, Fukuoka, 819-0395, Japan.
Mathematical models of immune responses have traditionally focused on adaptive immunity and pathogen-immune dynamics. However, recent advances in immunology have highlighted the critical role of innate immunity. In response to physical damage or pathogen attacks, innate immune cells circulating throughout the body rapidly migrate from blood vessels and accumulate at the site of injury, triggering inflammation.
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January 2025
Department of Mathematics, Vivekananda College, Kolkata, West Bengal, 700063, India.
The extinction of species is a major threat to the biodiversity. Allee effects are strongly linked to population extinction vulnerability. Emerging ecological evidence from numerous ecosystems reveals that the Allee effect, which is brought on by two or more processes, can work on a single species concurrently.
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January 2025
Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA.
We study Hopfield networks with non-reciprocal coupling inducing switches between memory patterns. Dynamical phase transitions occur between phases of no memory retrieval, retrieval of multiple point-attractors, and limit-cycle attractors. The limit cycle phase is bounded by two critical regions: a Hopf bifurcation line and a fold bifurcation line, each with unique dynamical critical exponents and sensitivity to perturbations.
View Article and Find Full Text PDFChaos
January 2025
Department of Mathematics, Indian Institute of Technology Patna, Patna 801103, India.
Human immunodeficiency virus (HIV) manifests multiple infections in CD4+ T cells, by binding its envelope proteins to CD4 receptors. Understanding these biological processes is crucial for effective interventions against HIV/AIDS. Here, we propose a mathematical model that accounts for the multiple infections of CD4+ T cells and an intracellular delay in the dynamics of HIV infection.
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