Research

Publications

Journals

1. H. Jardon-Kojakhmetov, C. Kuehn, I.P. Longo: Persistent synchronization of heterogeneous networks with time-dependent linear diffusive coupling, To appear in SIAM Journal on Applied Dynamical Systems (2024). 

2. I.P. Longo, C. Nuñez, R. Obaya: Critical transitions for scalar nonautonomous systems with concave nonlinearities: some rigorous estimates, Nonlinearity 37 045017 (2024). arXiv:2304.06417[math.DS]

3. J. Dueñas, I.P. Longo, R. Obaya: Rate-induced tracking for concave or d-concave transitions in a time-dependent environment with application in ecology, Chaos: An Interdisciplinary Journal of Nonlinear Science 33, 123113 (2023). arXiv:2305.14136[math.DS]

4. H. Krakovská, C. Kuehn, I.P. Longo: Resilience of dynamical systems. European Journal of Applied Mathematics 2024; 35(1):155-200. arXiv:2105.10592[math.DS]

5. I.P. Longo, R. Obaya, A.M. Sanz: Topologies of continuity for Carathéodory parabolic PDEs from a dynamical perspective. Discrete and Continuous Dynamical Systems 43, no.6 (2023), 2213-2240. arXiv:2209.03926[math.DS]  

6.  I.P. Longo, C. Nuñez, R. Obaya: Critical transitions in piecewise uniformly continuous concave quadratic ordinary differential equations.  To appear in Journal of Dynamics and Differential Equations (2023). arXiv:2110.10145 [math.DS]  

7. C. Kuehn, I.P. Longo: Estimating rate-induced tipping via asymptotic series and a Melnikov-like method. Nonlinearity 35 (2022), 2559–2587. arXiv:2011.04031v2 [math.DS]

8. I.P. Longo, S. Novo, R. Obaya: Monotone skew-product semiflows for Carathéodory differential equations and applications. Journal of Dynamics and Differential Equations 34, no.4 (2022), 2997–3033. arXiv:2007.13173 [math.DS]

9. I.P. Longo, C. Nuñez, R. Obaya, M. Rasmussen: Rate-induced tipping and saddle-node bifurcation for a class of quadratic differential equations with nonautonomous asymptotic dynamics. SIAM Journal on Applied Dynamical Systems 20, no. 1 (2021), 500-540. arXiv:2110.02608 [math.DS]

10. I.P. Longo, S. Novo, R. Obaya: Topologies of continuity for Carathéodory delay differential equations with applications in non-autonomous dynamics, Discrete and Continuous Dynamical Systems 39, no. 9 (2019), 5491-5520. arXiv:1901.03113 [math.DS]

11. I.P. Longo, S. Novo, R. Obaya: Weak topologies for Carathéodory differential equations: Continuous dependence, exponential Dichotomy and attractors, Journal of Dynamics and Differential Equations  31, no. 3 (2019), 1617-1651. arXiv:1709.06343 [math.DS]

12. I.P. Longo, S. Novo, R. Obaya, Topologies of L^p_loc type for Carathéodory functions with applications in non-autonomous differential equations, Journal of Differential Equations 263, no. 11 (2017), 7187-7220. arXiv: https://arxiv.org/abs/1705.00926

Other publications

• I.P. Longo: Topologies of continuity for Carathéodory differential equations with applications in non-autonomous dynamics, PhD thesis, Universidad de Valladolid, 2018.

Preprints and in progress

• C. Kuehn, I.P. Longo: On the homotopic deformation of periodic orbits in the van der Pol model.

• I.P. Longo, R. Skiba, C.Pötzsche: Global bifurcations of homoclinic solutions.

• I.P. Longo, M. Rasmussen: A boundary map approach to nonautonomous equations with bounded noise.

• I.P. Longo, R. Obaya, A.M. Sanz: Nonautonomous modelling in Energy Balance Models of climate. Limitations of averaging and climate sensitivity.

• I.P. Longo, R. Skiba, C.Pötzsche: Arzelà-Ascoli's theorem for Lebesgue measurable functions vanishing at infinity.

Scientific communications

Next invited talks

• June 24-28, 2024, Global bifurcations of homoclinic solutions for nonautonomous ordinary differential equations "XXVIII CEDYA", Bilbao, Spain.

• July 29-August 2, 2024, “XLIV Dynamics Days 2024”, Bremen, Germany.

• November 4-7, 2024 Plenary talk at 6th BYMAT Conference, Valladolid, Spain.

Past invited and contributed talks

• April 16th, 2024, Rigorous Criteria for Tipping and Tracking of Nonautonomous Concave Coercive Odes, Seminario di Dipartimento, Università del Salento (IT).

• November 15th, 2023, Nonautonomous tipping, safe margins and unsafe excursions, TiPES webinar (online).

• October 23rd, 2023, Persistent synchronization of heterogeneous networks with time-dependent linear diffusive coupling, Technical University Munich (DE).

• October 17, 2023, Rate-induced tracking and EWS for concave and d-concave nonautonomous scalar differential equations, Non-autonomous Dynamics in Complex Systems: Theory and Applications to Critical Transitions: NADCOM, Dresden Max-Planck-Institute for Physics of Complex Systems (DE).

• September 14th, 2023, Persistent synchronization of heterogeneous networks with time-dependent linear diffusive coupling, Dynamics Days Europe, Napoli (IT).

• May 14, 2023, Rigorous Criteria for Tipping and Tracking of Concave Coercive Odes, SIAM Conference on Applications of Dynamical Systems (DS23), Portland (USA).

• March 7, 2023, A bifurcation approach to rate-induced tipping for scalar ODEs, Weekly DynamIC seminar, Imperial College London (UK).

• June 27th, 2022, A path towards classifying rate-induced tipping as a nonautonomous bifurcation, Oberseminar Dynamics, Technical University Munich (DE).

• June 20th, 2022, Rate-induced tipping as a nonautonomous saddle-node bifurcation in a class of scalar quadratic ODEs, Department seminar, Alpen-Adria Universität, Klagenfurt (AUT).

• May 24th, 2022, A path towards classifying rate-induced tipping as a nonautonomous bifurcation, Department seminar, Freie Universitaet Berlin (DE).

• March 16th, 2022, A path towards classifying rate-induced tipping as a nonautonomous bifurcation, Department seminar, Universidad de Valladolid (SP).

• March 8th, 2022, A path towards classifying rate-induced tipping as a nonautonomous bifurcation, Floris Takens Seminar, University of Groningen (NL).

• January 20th, 2022, Rate-induced tipping as a nonautonomous saddle-node bifurcation in a class of scalar quadratic ODEs with nonautonomous asymptotic dynamics, Biennial Congress of the Royal Spanish Mathematical Society, Ciudad Real (SP).

• July 14th, 2021, Rate-induced tipping and saddle-node bifurcation in a class of scalar quadratic nonautonomous ODEs, Weekly seminar, Universidade de São Paulo (BR).

• July 5th, 2021, Rate-induced tipping as a nonautonomous bifurcation in a class of scalar quadratic ODEs, EPSRC Meeting "Nonautonomous dynamical systems: from theory to applications", University of Exeter (UK).

• May 23, 2021, Resilience in dynamical systems: classic and newer concepts, SIAM Dynamical Systems 2021 in the minisymposium "Recent developments in ecosystem resilience" (USA).

• March 16, 2021, Strong and weak topologies for Carathéodory functions with applications in the study of non-autonomous ODEs, Floris Takens Seminar, University of Groningen (NL).

• March 13-14, 2021, Topologies of continuity for Carathéodory delay differential equations with applications in non-autonomous dynamics, AMS Spring Southeastern Sectional Meeting, special session on "Functional differential equations, theory and applications" (USA).

• August 26, 2020, Monotone skew-product semiflows for Carathéodory delay differential equations and applications, Dynamics Days Digital 2020 (online).

• July 31, 2020, Estimating the occurrence of a rate-induced tipping via asymptotic series expansions and a Melnikov-like method, Critical Transitions in Complex Systems 2020 (online). 

• May 23, 2019, Study of Attractors for Compartmental Systems Modeled with Carathéodory Differential Equations, SIAM Conference on Applications of Dynamical Systems (DS19), Snowbird (USA).

• March 24, 2019,  An overview on Carathéodory dynamical systems: recent results and new challenges, CRITICS Workshop "Critical Transitions in Complex Systems", London (UK).

• August 6, 2018, Topologies of continuity for skew-product flows induced by Carathéodory ODEs, and applications, invited by Prof. C. Kuehn, Technische Universität München (DE).

• September 15, 2018, Comparison methods and propagation of stability properties for Carathéodory compartmental systems, Jornada de doctorandos en Matemáticas 2018, Valladolid (SP).

• March 13, 2018, Study of stability of Carathéodory compartmental systems, CRITICS Workshop "Mathematical theory and applications", Wöltingerode (DE).

• September 14, 2017,  Strong and weak L^p_loc-type topologies for Carathéodory functions with applications in the study of non-autonomous ODEs, CRITICS Summer Meeting 2017, Valladolid (SP).

• August 4, 2017, A brief survey on Carathéodory topological spaces and ODEs, CRITICS "Gathering in Finland", Helsinky (FIN).

• July 7, 2017, Study of attractors of Carathéodory differential equations, Jornada de doctorandos en Matemáticas 2017, Valladolid (SP).

• June 5, 2017, Strong and weak topologies for Carathéodory functions with applications in the study of the attractors of non-autonomous differential equations, International Conference on Differential \& Difference Eq. and Applications, Amadora (P).

• March 30, 2017, Non-autonomous modelization and attractors: the Carathéodory case, invited by Prof. H. Dijkstra Institute for Marine and Atmospheric Research Utrecht (IMAU), Utrecht (NL).

• March 28, 2017, Carathéodory differential equations: topological dynamics and modelization, CRITICS Workshop "Bridging mathematics and practice", Soesterberg (NL).

• September 8, 2016, Topological dynamics of non-autonomous differential equations of Carathéodory type, CRITICS Workshop "Mathematical Theory and applications", Kulhuse (DK).

Posters

• March 11, 2020, Rate-induced tipping. Controlling a critical transition, EuroTech Postdoc workshop, Lyngby (DK).

• March 24, 2019,  An application of continuity of the skew-product flow for Carathéodory ODEs: the linearized skew-product flow, CRITICS Workshop "Critical Transitions in Complex Systems", London (UK).

• August 28, 2018, Linearized skew-product flows for Carathéodory ODEs, CRITICS Workshop "Critical transitions or Tipping points, Cork (IRL).

Organized events (next events in bold)

• Workshop "Critical transitions and nonautonomous bifurcations", Technical University of Munich Science & Study Center, 24th-26th of August 2022 (co-organized with C. Kühn and M. Manlik). 

• Special session "Nonautonomous dynamical systems and applications" at the 2022 biennial meeting of the Royal Spanish Mathematical Society, 17th-21st of January 2022 (co-organized with Victor M. Muñoz, Sylvia Novo, Rafael Obaya). 

• Invited minisymposium "Non-autonomous dynamics and applications" at Dynamic Days Digital 2020. 

• Minisymposium ``Nonautonomous transitions and bifurcations'' at Dynamics Days Europe 2020 (co-organized with C. Kühn) - Postponed to 2021 due to COVID19 -

• 2017 CRITICS Summer meeting held in Valladolid (SP) on 4th-15th of September 2017. (Organizing Committee)

• 2017 CRITICS Spring Doctoral School held in Lecce (IT) on 18th-22nd of April 2017. (Organizing and Scientific Committee)