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Neuronal firing is crucial to the information processing in the nervous system. In order to make a further study of bifurcation scenarios, experiments were performed on neural pacemakers formed at the injured site of rat sciatic nerve subjected to chronic ligatures. We chose the conductance of voltage-dependent potassium ion channels as conditional parameter, and the extracellular calcium concentration as bifurcation parameter, to give a demonstration of how the firing pattern of neural pacemaker responses to dual parameter adjusting. Among 28 preparations observed, 21 were insensitive to dual parameter adjusting since no change of bifurcation scenario structure was detected. On the contrary, the residual 7 preparations showed dramatic bifurcation scenario shifting corresponding to different dual parameter configuration. Briefly, when concentration of 4-aminopyridine (4-AP), a voltage-dependent potassium ion channels blocker, was kept at different level and extracellular Ca2+ concentration was decreased gradually, different bifurcation scenarios of firing patterns were exhibited in an identical neural pacemaker. The two-parameter bifurcation scenarios of experimental neural pacemaker with different parameter configuration were also different. The results show that neural firing pattern is different when the parameter configuration is different, and the bifurcation scenario is a fundamental framework to identify the transitions between firing patterns.
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Chaos
September 2025
School of Engineering, University of Applied Sciences of Western Switzerland HES-SO, CH-1950 Sion, Switzerland.
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View Article and Find Full Text PDFMedicina (Kaunas)
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Emergency Clinical Hospital Dr. Bagdasar-Arseni, 041915 Bucharest, Romania.
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View Article and Find Full Text PDFMathematics (Basel)
March 2025
Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA.
This article is concerned with the mathematical modeling of cancer virotherapy, emphasizing the impact of Allee effects on tumor cell growth. We propose a modeling framework that describes the complex interaction between tumor cells and oncolytic viruses. The efficacy of this therapy against cancer is mathematically investigated.
View Article and Find Full Text PDFNat Hazards (Dordr)
July 2025
University of Twente, Enschede, The Netherlands.
Hydrodynamic models can provide accurate information on the consequences of a dike breach, but their long computation times hinder the analysis of uncertainties and scenarios during a time-sensitive emergency situation. Conceptual models use simplified rules and relations, and allow for much faster computation while preserving reasonable accuracy. In this study, we develop a conceptual model with breach growth that estimates the dike breach outflow for varying river discharge events and for varying dike breach locations along the Rhine's bifurcations in the Netherlands and Germany.
View Article and Find Full Text PDFJ Math Biol
August 2025
Center for Applied Mathematics, Cornell University, Ithaca, NY, 14853, USA.
Many animals show avoidance behavior in response to disease. For instance, in some species of frogs, individuals that survive infection of the fungal disease chytridiomycosis may learn to avoid areas where the pathogen is present. As chytridiomycosis has caused substantial declines in many amphibian populations worldwide, it is a highly relevant example for studying these behavioral dynamics.
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