Publications

Preprints

I.P. Longo, R. Obaya, A.M. Sanz. Nonautonomous modelling in Energy Balance Models of climate. Limitations of averaging and climate sensitivity. 03/2025
C. Elia, R. Fabbri, C. Núñez. Global bifurcation diagrams for coercive third-degree polynomial ordinary differential equations with recurrent nonautonomous coefficients. 01/2025
J. Dueñas, C. Núñez, R. Obaya. Concave-convex nonautonomous scalar ordinary differential equations: from bifurcation theory to critical transitions. 12/2024
I.P. Longo, R. Skiba, C.Pötzsche. Global bifurcations of homoclinic solutions. 09/2024.

2025

M. Kryspin, J. Mierczynski, S. Novo, R. Obaya. Two dynamical approaches to the notion of exponential separation for random systems of delay differential equations. Published online on Proceedings of the Royal Society of Edinburgh.
J. Dueñas, C. Núñez, R. Obaya. Saddle-node bifurcations for concave in measure and d-concave in measure skewproduct flows with applications to population dynamics and circuits. Communications in Nonlinear Science and Numerical Simulation 142, 108577 (2025).
I.P. Longo, R. Obaya, A.M. Sanz. Tracking nonautonomous attractors in singularly perturbed systems of ODEs with dependence on the fast time. Journal of Differential Equations 414 (1), 609–644 (2025).

2024

I.P. Longo, E. Queirolo, C. Kuehn. On the transition between autonomous and nonautonomous systems: the case of FitzHugh-Nagumo’s model. Chaos 34, 123171 (2024).
J. Dueñas, C. Núñez, R. Obaya. Critical transitions for asymptotically concave or d-concave nonautonomous differential equations with applications in ecology. Journal of Nonlinear Science 34, 105 (2024).
I.P. Longo, C. Núñez, R. Obaya. Critical transitions in piecewise uniformly continuous concave quadratic differential equations. Journal of Dynamics and Differential Equations 36, 2153–2192 (2024).
J.A. Langa, R. Obaya, A.N. Oliveira-Sousa. New notion of nonuniform exponential dichotomy with applications to the theory of pullback and forward attractors. Nonlinearity 37 (10), 105009 (2024).
H. Jardón-Kojakhmetov, C. Kuehn, I.P. Longo. Persistent synchronization of heterogeneous networks with time-dependent linear diffusive coupling. SIAM Journal on Applied Dynamical Systems 23 (2), 1540-1578 (2024).
S. Novo, R. Obaya, A.M. Sanz, V.M. Villarragut. The exponential ordering for nonautonomous delay systems with applications to compartmental Nicholson systems. Proceedings of the Royal Society of Edinburgh Section A: Mathematics 154 (2), 568-599 (2024).
I.P. Longo, C. Núñez, R. Obaya. Critical transitions for scalar nonautonomous systems with concave nonlinearities: some rigorous estimates. Nonlinearity 37 (4), 045017 (2024).
H. Krakovská, C. Kuehn, I.P. Longo. Resilience of dynamical systems. European Journal of Applied Mathematics 35 (1), 155-200 (2024).
J. Dueñas, C. Núñez, R. Obaya. Generalized pitchfork bifurcations in d-concave nonautonomous scalar ordinary differential equations. Journal of Dynamics and Differential Equations 36, 3125–3157 (2024).

2023

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 33 (12), 123113 (2023).
A.M. Sanz, V.M. Villarragut. Attractors in almost periodic Nicholson systems and some numerical simulations. Journal of Mathematical Analysis and Applications 528 (1), 127588 (2023).
J. Dueñas, C. Núñez, R. Obaya. Critical transitions in d-concave nonautonomous scalar ordinary differential equations appearing in population dynamics. SIAM Journal on Applied Dynamical Systems 22 (4), 2649-2692 (2023).
J. Campos, C. Núñez, R. Obaya. Uniform stability and chaotic dynamics in nonhomogeneous linear dissipative scalar ordinary differential equations. Journal of Differential Equations 361, 248-287 (2023).
J. Dueñas, C. Núñez, R. Obaya. Bifurcation theory of attractors and minimal sets in d-concave nonautonomous scalar ordinary differential equations. Journal of Differential Equations 361, 138-182 (2023).
I.P. Longo, R. Obaya, A.M. Sanz. Topologies of continuity for Carathéodory parabolic PDEs from a dynamical perspective. Discrete and Continuous Dynamical Systems Series A 43 (6), 2213-2240 (2023).

2022

I.P. Longo, S. Novo, R. Obaya. Monotone skew-product semiflows for Carathéodory differential equations and applications. Journal of Dynamics and Differential Equations 34 (4), 2997-3033 (2022).
C. Kuehn, I.P. Longo. Estimating rate-induced tipping via asymptotic series and a Melnikov-like method. Nonlinearity 35 (5), 2559-2587 (2022).
S. Novo, V.M. Villarragut. Long-term behavior of nonautonomous neutral compartmental systems. Electronic Journal of Qualitative Theory of Differential Equations 7, 1-19 (2022).

2021

R. Obaya, A.M. Sanz. Non-autonomous scalar linear-dissipative and purely dissipative parabolic PDEs over a compact base flow. Journal of Differential Equations 285, 714-750 (2021).
I.P. Longo, C. Núñez, R. Obaya, M. Rasmussen. Rate-induced tipping and saddle-node bifurcation for quadratic differential equations with nonautonomous asymptotic dynamics. SIAM Journal on Applied Dynamical Systems 20 (1), 500-540 (2021).

2020

R. Fabbri, C. Núñez. On the solvavility of the Yakubovich linear-quadratic infinite horizon minimization problem. Annali di Matematica Pura ed Applicata 199 (5), 1713-1735 (2020).
S. Novo, R. Obaya, V.M. Villarragut. Asymptotic behavior of solutions of nonautonomous neutral dynamical systems. Nonlinear Analysis, Theory, Methods and Applications 199, 111918 (2020).
J.A. Langa, R. Obaya, A.M. Sanz. Forwards attraction properties in scalar non-autonomous linear-dissipative parabolic PDEs. The case of null upper Lyapunov exponent. Nonlinearity 33 (9), 4277-4309 (2020).
J. Mierczynski, S. Novo, R. Obaya. Lyapunov exponents and Oseledets decomposition in random dynamical systems generated by systems of delay differential equations. Communications on Pure and Applied Analysis 19 (4), 2235-2255 (2020).

2019

C. Elia, I. Maroto, C. Núñez, R. Obaya. Existence of global attractor for a nonautonomous state-dependent delay differential equation of neuronal type. Communications in Nonlinear Science and Numerical Simulation 78, 104874 (2019).
C. Núñez, R. Obaya. Li-Yorke chaos in nonautonomous Hopf bifurcation patters-I. Nonlinearity 32 (10), 3940-3980 (2019).
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 Series A 39 (9), 5491-5520 (2019).
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 (3), 1617-1651 (2019).
C. Núñez, R. Obaya. Non-Atkinson perturbations of nonautonomous linear Hamiltonian systems: exponential dichotomy and nonoscillation. Journal of Dynamics and Differential Equations 31 (3), 1397-1426 (2019).
R. Obaya, A.M. Sanz. Persistence in non-autonomous quasimonotone parabolic partial functional differential equations with delay. Discrete and Continuous Dynamical Systems Series B 24 (8), 3947-3970 (2019).

2018

J. Mierczynski, S. Novo, R. Obaya. Principal Floquet subspaces and exponential separations of type II with applications to random delay differential equations. Discrete and Continuous Dynamical Systems Series A 38 (12), 6163-6193 (2018).
T. Caraballo, J.A. Langa, R. Obaya, A.M. Sanz. Global and cocycle attractors for non-autonomous reaction-diffusion equations. The case of null upper Lyapunov exponent. Journal of Differential Equations 265 (9), 3914-3951.
T. Faria, R. Obaya, A.M. Sanz. Asymptotic behaviour for a class of non-monotone delay differential systems with applications. Journal of Dynamics and Differential Equations 30 (3), 911-935 (2018).
R. Obaya, A.M. Sanz. Is uniform persistence a robust property in almost periodic models? A well-behaved family: Almost-periodic Nicholson systems. Nonlinearity 31 (2), 388-413 (2018).

2017

I.P. Longo, S. Novo, R. Obaya. Topologies of L_loc^p type for Carathéodory functions with applications in non-autonomous differential equations. Journal of Differential Equations 263 (11), 7187-7220 (2017).
I. Maroto, C. Núñez, R. Obaya. Exponential stability for nonautonomous functional differential equations with state-dependent delay. Discrete and Continuous Dynamical Systems Series B 22 (8), 3167-3197 (2017).
I. Maroto, C. Núñez, R. Obaya. Dynamical properties of nonautonomous functional differential equations with state-dependent delay. Discrete and Continuous Dynamical Systems Series A 37 (7), 3939-3961 (2017).
J. Campos, R. Obaya, M. Tarallo. Favard theory and Fredhold Alternative for disconjugate recurrent second order equations. Communications on Pure and Applied Analysis 16 (4), 1199-1232 (2017).
J. Campos, R. Obaya, M. Tarallo. Favard theory for the adjoint equation and Fredholm Alternative. Journal of Differential Equations 262 (2), 749-802 (2017).
T. Caraballo, J.A. Langa, R. Obaya. Pullback, forward and chaotic dynamics in 1D non-autonomous linear-dissipative equations. Nonlinearity 30 (1), 274-299 (2017).

2016

M. Franca, R. Johnson, V.M. Villarragut. On the nonautonomous Hopf bifurcation problem. Discrete and Continuous Dynamical Systems Series S 9 (4), 1119-1148 (2016).
R. Obaya, A.M. Sanz. Uniform and strict persistence in monotone skew-product semiflows with applications to non-autonomous Nicholson systems. Journal of Differential Equations 261 (7), 4135-4163 (2016).
J. Campos, R. Obaya, M. Tarallo. Recurrent equations with sign and fredholm alternative. Discrete and Continuous Dynamical Systems Series S 9 (4), 959-977 (2016).
R. Fabbri, S. Novo, C. Núñez, R. Obaya. Null controllable sets and reachable sets for nonautonomous linear control systems. Discrete and Continuous Dynamical Systems Series S 9 (4), 1069-1094 (2016).
C.A. Cardoso, J.A. Langa, R. Obaya. Characterization of cocycle attractors for nonautonomous reaction-diffusion equations. International Journal of Bifurcation and Chaos 26 (8), 1650135 (2016).
R. Johnson, R. Fabbri, S. Novo, C. Núñez, R. Obaya. Preface. Discrete and Continuous Dynamical Systems Series S 9 (4), i-iii (2016).
R. Johnson, R. Obaya, S. Novo, C. Núñez, R. Fabbri. Nonautonomous linear Hamiltonian systems. Developments in Mathematics 36, 2016.