Saddle-node bifurcations for concave in measure and d-concave in measure skewproduct flows with applications to population dynamics and circuits
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| Format: | Preprint |
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2024
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| _version_ | 1866910774834757632 |
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| author | Dueñas, Jesús Núñez, Carmen Obaya, Rafael |
| author_facet | Dueñas, Jesús Núñez, Carmen Obaya, Rafael |
| contents | Concave in measure and d-concave in measure nonautonomous scalar ordinary differential equations given by coercive and time-compactible maps have similar properties to equations satisfying considerably more restrictive hypotheses. This paper describes the generalized simple or double saddle-node bifurcation diagrams for one-parametric families of equations of these types, from which the dynamical possibilities for each of the equations follow. This new framework allows the analysis of ``almost stochastic" equations, whose coefficients vary in very large chaotic sets. The results also apply to the analysis of the occurrence of critical transitions for a range of models much larger than in previous approaches. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_15515 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Saddle-node bifurcations for concave in measure and d-concave in measure skewproduct flows with applications to population dynamics and circuits Dueñas, Jesús Núñez, Carmen Obaya, Rafael Dynamical Systems 37B55, 37G35, 37N25, 37N20 Concave in measure and d-concave in measure nonautonomous scalar ordinary differential equations given by coercive and time-compactible maps have similar properties to equations satisfying considerably more restrictive hypotheses. This paper describes the generalized simple or double saddle-node bifurcation diagrams for one-parametric families of equations of these types, from which the dynamical possibilities for each of the equations follow. This new framework allows the analysis of ``almost stochastic" equations, whose coefficients vary in very large chaotic sets. The results also apply to the analysis of the occurrence of critical transitions for a range of models much larger than in previous approaches. |
| title | Saddle-node bifurcations for concave in measure and d-concave in measure skewproduct flows with applications to population dynamics and circuits |
| topic | Dynamical Systems 37B55, 37G35, 37N25, 37N20 |
| url | https://arxiv.org/abs/2407.15515 |