#dynamicalsystems — Public Fediverse posts

RE: https://mathstodon.xyz/@DurstewitzLab/116549716016889895

🧠 New preprint by Brändle et al./ @DurstewitzLab: Continuous-Time Piecewise-Linear #RecurrentNeuralNetworks introduces continuous-time #PLRNNs for #DynamicalSystems reconstruction.

The model combines interpretability and analytical tractability of pw-linear #RNN with cont.-time dynamics, allowing semi-analytic analysis of equilibria and limit cycles while handling irregularly sampled data better than standard Neural #ODEs.

#NeuralDynamics #Neuroscience #NeuralODE

RE: https://mathstodon.xyz/@DurstewitzLab/116549716016889895

🧠 New preprint by Brändle et al./ @DurstewitzLab: Continuous-Time Piecewise-Linear #RecurrentNeuralNetworks introduces continuous-time #PLRNNs for #DynamicalSystems reconstruction.

The model combines interpretability and analytical tractability of pw-linear #RNN with cont.-time dynamics, allowing semi-analytic analysis of equilibria and limit cycles while handling irregularly sampled data better than standard Neural #ODEs.

#NeuralDynamics #Neuroscience #NeuralODE

RE: https://mathstodon.xyz/@DurstewitzLab/116549716016889895

🧠 New preprint by Brändle et al./ @DurstewitzLab: Continuous-Time Piecewise-Linear #RecurrentNeuralNetworks introduces continuous-time #PLRNNs for #DynamicalSystems reconstruction.

The model combines interpretability and analytical tractability of pw-linear #RNN with cont.-time dynamics, allowing semi-analytic analysis of equilibria and limit cycles while handling irregularly sampled data better than standard Neural #ODEs.

#NeuralDynamics #Neuroscience #NeuralODE

RE: https://mathstodon.xyz/@DurstewitzLab/116549716016889895

🧠 New preprint by Brändle et al./ @DurstewitzLab: Continuous-Time Piecewise-Linear #RecurrentNeuralNetworks introduces continuous-time #PLRNNs for #DynamicalSystems reconstruction.

The model combines interpretability and analytical tractability of pw-linear #RNN with cont.-time dynamics, allowing semi-analytic analysis of equilibria and limit cycles while handling irregularly sampled data better than standard Neural #ODEs.

#NeuralDynamics #Neuroscience #NeuralODE

RE: https://mathstodon.xyz/@DurstewitzLab/116549716016889895

🧠 New preprint by Brändle et al./ @DurstewitzLab: Continuous-Time Piecewise-Linear #RecurrentNeuralNetworks introduces continuous-time #PLRNNs for #DynamicalSystems reconstruction.

The model combines interpretability and analytical tractability of pw-linear #RNN with cont.-time dynamics, allowing semi-analytic analysis of equilibria and limit cycles while handling irregularly sampled data better than standard Neural #ODEs.

#NeuralDynamics #Neuroscience #NeuralODE

New paper, with Zerong Guo, Zonghua Liu, Shuguang Guan, Stefano Boccaletti and Jie Zhou.

Everyone knows about chimera states. We show a new mechanism for the emergence of chimeras that is specific of higher-order interactions. Interestingly, this mechanism is somewhat analogous to what happens in some proteins with intrinsic disorder (which we showed a couple of years ago), so we called it intrinsic frustration.

#mathematics #physics #science #HigherOrderNetworks #synchronization #DynamicalSystems #ChimeraStates #chimeras #frustration #IntrinsicDisorder

New paper, with Zerong Guo, Zonghua Liu, Shuguang Guan, Stefano Boccaletti and Jie Zhou.

Everyone knows about chimera states. We show a new mechanism for the emergence of chimeras that is specific of higher-order interactions. Interestingly, this mechanism is somewhat analogous to what happens in some proteins with intrinsic disorder (which we showed a couple of years ago), so we called it intrinsic frustration.

#mathematics #physics #science #HigherOrderNetworks #synchronization #DynamicalSystems #ChimeraStates #chimeras #frustration #IntrinsicDisorder

New paper, with Zerong Guo, Zonghua Liu, Shuguang Guan, Stefano Boccaletti and Jie Zhou.

Everyone knows about chimera states. We show a new mechanism for the emergence of chimeras that is specific of higher-order interactions. Interestingly, this mechanism is somewhat analogous to what happens in some proteins with intrinsic disorder (which we showed a couple of years ago), so we called it intrinsic frustration.

#mathematics #physics #science #HigherOrderNetworks #synchronization #DynamicalSystems #ChimeraStates #chimeras #frustration #IntrinsicDisorder

New paper, with Zerong Guo, Zonghua Liu, Shuguang Guan, Stefano Boccaletti and Jie Zhou.

Everyone knows about chimera states. We show a new mechanism for the emergence of chimeras that is specific of higher-order interactions. Interestingly, this mechanism is somewhat analogous to what happens in some proteins with intrinsic disorder (which we showed a couple of years ago), so we called it intrinsic frustration.

#mathematics #physics #science #HigherOrderNetworks #synchronization #DynamicalSystems #ChimeraStates #chimeras #frustration #IntrinsicDisorder

New paper, with Zerong Guo, Zonghua Liu, Shuguang Guan, Stefano Boccaletti and Jie Zhou.

Everyone knows about chimera states. We show a new mechanism for the emergence of chimeras that is specific of higher-order interactions. Interestingly, this mechanism is somewhat analogous to what happens in some proteins with intrinsic disorder (which we showed a couple of years ago), so we called it intrinsic frustration.

#mathematics #physics #science #HigherOrderNetworks #synchronization #DynamicalSystems #ChimeraStates #chimeras #frustration #IntrinsicDisorder

New paper, with Kirill Kovalenko, Gonzalo Contreras, Stefano Boccaletti and Rubén Sánchez.

People have noticed that, in higher-order networks, synchronization is often explosive, and that cluster synchronization happens very rarely, if ever. We explain why, by showing that symultaneous dynamical equitability across layers or interaction orders is necessary and sufficient for cluster synchronization, except if the coupling functions depend linearly on each other. Since the probability of randomly satisfying this condition is exceedingly low, cluster synchronization is precluded in such networks.

https://www.nature.com/articles/s42005-026-02543-5

#mathematics #physics #science #networks #complexity #HigherOrderNetworks #MultiplexNetworks #synchronization #dynamicalsystems #graphs #graphtheory #equitability #ClusterSynchronization #ExplosiveSynchronization

New paper, with Kirill Kovalenko, Gonzalo Contreras, Stefano Boccaletti and Rubén Sánchez.

People have noticed that, in higher-order networks, synchronization is often explosive, and that cluster synchronization happens very rarely, if ever. We explain why, by showing that symultaneous dynamical equitability across layers or interaction orders is necessary and sufficient for cluster synchronization, except if the coupling functions depend linearly on each other. Since the probability of randomly satisfying this condition is exceedingly low, cluster synchronization is precluded in such networks.

https://www.nature.com/articles/s42005-026-02543-5

#mathematics #physics #science #networks #complexity #HigherOrderNetworks #MultiplexNetworks #synchronization #dynamicalsystems #graphs #graphtheory #equitability #ClusterSynchronization #ExplosiveSynchronization

New paper, with Kirill Kovalenko, Gonzalo Contreras, Stefano Boccaletti and Rubén Sánchez.

People have noticed that, in higher-order networks, synchronization is often explosive, and that cluster synchronization happens very rarely, if ever. We explain why, by showing that symultaneous dynamical equitability across layers or interaction orders is necessary and sufficient for cluster synchronization, except if the coupling functions depend linearly on each other. Since the probability of randomly satisfying this condition is exceedingly low, cluster synchronization is precluded in such networks.

https://www.nature.com/articles/s42005-026-02543-5

#mathematics #physics #science #networks #complexity #HigherOrderNetworks #MultiplexNetworks #synchronization #dynamicalsystems #graphs #graphtheory #equitability #ClusterSynchronization #ExplosiveSynchronization

New paper, with Kirill Kovalenko, Gonzalo Contreras, Stefano Boccaletti and Rubén Sánchez.

People have noticed that, in higher-order networks, synchronization is often explosive, and that cluster synchronization happens very rarely, if ever. We explain why, by showing that symultaneous dynamical equitability across layers or interaction orders is necessary and sufficient for cluster synchronization, except if the coupling functions depend linearly on each other. Since the probability of randomly satisfying this condition is exceedingly low, cluster synchronization is precluded in such networks.

https://www.nature.com/articles/s42005-026-02543-5

#mathematics #physics #science #networks #complexity #HigherOrderNetworks #MultiplexNetworks #synchronization #dynamicalsystems #graphs #graphtheory #equitability #ClusterSynchronization #ExplosiveSynchronization

New paper, with Kirill Kovalenko, Gonzalo Contreras, Stefano Boccaletti and Rubén Sánchez.

People have noticed that, in higher-order networks, synchronization is often explosive, and that cluster synchronization happens very rarely, if ever. We explain why, by showing that symultaneous dynamical equitability across layers or interaction orders is necessary and sufficient for cluster synchronization, except if the coupling functions depend linearly on each other. Since the probability of randomly satisfying this condition is exceedingly low, cluster synchronization is precluded in such networks.

https://www.nature.com/articles/s42005-026-02543-5

#mathematics #physics #science #networks #complexity #HigherOrderNetworks #MultiplexNetworks #synchronization #dynamicalsystems #graphs #graphtheory #equitability #ClusterSynchronization #ExplosiveSynchronization

Systems don’t just collapse … they can be tested before they do. This pre-registered pipeline defines a falsification-first empirical test of the #CRTI framework on the Peter Lake regime shift dataset. doi.org/10.5281/zeno... #EarlyWarning #DynamicalSystems #ComplexSystems 🖖

CRTI Empirical Validation Pipe...

Systems rarely collapse out of nowhere … they cross invisible boundaries first. This paper shows why those boundaries must exist in competitive adaptive systems and how a simple index T = R/\Phi can locally signal proximity. doi.org/10.5281/zeno... #ComplexSystems #EarlyWarning #DynamicalSystems 🖖

Bistability and Basin Classifi...

CRTI 2.2 moves systemic stress diagnostics from a scalar heuristic to a spectral stability model … doi.org/10.5281/zeno... #ComplexityScience #ControlTheory #Dynamical-Systems #SystemsTheory #CRTI #CRTI2.2 🖖

CRTI 2.2 moves systemic stress diagnostics from a scalar heuristic to a spectral stability model … doi.org/10.5281/zeno... #ComplexityScience #ControlTheory #Dynamical-Systems #SystemsTheory #CRTI #CRTI2.2 🖖

CRTI 2.2 moves systemic stress diagnostics from a scalar heuristic to a spectral stability model … doi.org/10.5281/zeno... #ComplexityScience #ControlTheory #Dynamical-Systems #SystemsTheory #CRTI #CRTI2.2 🖖

CRTI 2.2 extends scalar systemic stress diagnostics into a fully anisotropic matrix stability framework, enabling eigenvalue-based detection of directionalinstability in complex adaptivesystems. Zenodo: doi.org/10.5281/zeno... #ComplexityScience #ControlTheory #DynamicalSystems #SystemsTheory #CRTI

CRTI 2.2: An Anisotropic Matri...

CRTI 2.2 extends scalar systemic stress diagnostics into a fully anisotropic matrix stability framework, enabling eigenvalue-based detection of directionalinstability in complex adaptivesystems. Zenodo: doi.org/10.5281/zeno... #ComplexityScience #ControlTheory #DynamicalSystems #SystemsTheory #CRTI

CRTI 2.2: An Anisotropic Matri...

CRTI 2.2 extends scalar systemic stress diagnostics into a fully anisotropic matrix stability framework, enabling eigenvalue-based detection of directionalinstability in complex adaptivesystems. Zenodo: doi.org/10.5281/zeno... #ComplexityScience #ControlTheory #DynamicalSystems #SystemsTheory #CRTI

CRTI 2.2: An Anisotropic Matri...

#NeuralDynamics is a central subfield of #ComputationalNeuroscience studying timedependent #NeuralActivity and its governing #mathematics. It examines how #NeuralStates evolve, how stable or unstable patterns arise, and how #learning reshapes them. Neural dynamics forms the backbone for how #neurons & #NeuralNetworks generate complex activity over time. This post gives a brief overview of the field & its historical milestones:

🌍https://www.fabriziomusacchio.com/blog/2026-02-04-neural_dynamics/

#CompNeuro #Neuroscience #DynamicalSystems

Is there a #mathematical framework for abrupt change? Christopher Zeeman was one of the key figures behind #CatastropheTheory, a topological approach to discontinuous behavior that later informed much of today’s work on #TippingPoints. Just came across his elegant 1976 paper, outlining his core ideas:

📄 https://www.jstor.org/stable/24950329

#DynamicalSystems #Topology #ComplexSystems

Oh this is fun!

#DynamicalSystems #Attractor #StrangeAttractors @maxpool https://mathstodon.xyz/@maxpool/115473317560499952

Oh this is fun!

#DynamicalSystems #Attractor #StrangeAttractors @maxpool https://mathstodon.xyz/@maxpool/115473317560499952

Oh this is fun!

#DynamicalSystems #Attractor #StrangeAttractors @maxpool https://mathstodon.xyz/@maxpool/115473317560499952

Oh this is fun!

#DynamicalSystems #Attractor #StrangeAttractors @maxpool https://mathstodon.xyz/@maxpool/115473317560499952

Oh this is fun!

#DynamicalSystems #Attractor #StrangeAttractors @maxpool https://mathstodon.xyz/@maxpool/115473317560499952

🧠 New preprint by Behrad et al. introducing #fastDSA, a much faster way to compare neural systems at the level of their dynamics, not just geometry or task performance.

What’s cool here: similarity is defined by shared #VectorFields, i.e. by the computational mechanism itself. This provides the first tool for mechanistic comparison of neural computations (to my knowledge).

🌍 https://arxiv.org/abs/2511.22828
💻 https://github.com/CMC-lab/fastDSA

#Neuroscience #CompNeuro #NeuralDynamics #Manifolds #DynamicalSystems

🧠 New preprint by Behrad et al. introducing #fastDSA, a much faster way to compare neural systems at the level of their dynamics, not just geometry or task performance.

What’s cool here: similarity is defined by shared #VectorFields, i.e. by the computational mechanism itself. This provides the first tool for mechanistic comparison of neural computations (to my knowledge).

🌍 https://arxiv.org/abs/2511.22828
💻 https://github.com/CMC-lab/fastDSA

#Neuroscience #CompNeuro #NeuralDynamics #Manifolds #DynamicalSystems

🧠 New preprint by Behrad et al. introducing #fastDSA, a much faster way to compare neural systems at the level of their dynamics, not just geometry or task performance.

What’s cool here: similarity is defined by shared #VectorFields, i.e. by the computational mechanism itself. This provides the first tool for mechanistic comparison of neural computations (to my knowledge).

🌍 https://arxiv.org/abs/2511.22828
💻 https://github.com/CMC-lab/fastDSA

#Neuroscience #CompNeuro #NeuralDynamics #Manifolds #DynamicalSystems

🧠 New preprint by Behrad et al. introducing #fastDSA, a much faster way to compare neural systems at the level of their dynamics, not just geometry or task performance.

What’s cool here: similarity is defined by shared #VectorFields, i.e. by the computational mechanism itself. This provides the first tool for mechanistic comparison of neural computations (to my knowledge).

🌍 https://arxiv.org/abs/2511.22828
💻 https://github.com/CMC-lab/fastDSA

#Neuroscience #CompNeuro #NeuralDynamics #Manifolds #DynamicalSystems

🧠 New preprint by Behrad et al. introducing #fastDSA, a much faster way to compare neural systems at the level of their dynamics, not just geometry or task performance.

What’s cool here: similarity is defined by shared #VectorFields, i.e. by the computational mechanism itself. This provides the first tool for mechanistic comparison of neural computations (to my knowledge).

🌍 https://arxiv.org/abs/2511.22828
💻 https://github.com/CMC-lab/fastDSA

#Neuroscience #CompNeuro #NeuralDynamics #Manifolds #DynamicalSystems

Representation learning often emphasizes metric preservation. We instead build Symplectic structural invariance directly into the representation.

https://arxiv.org/abs/2512.19409

We embed Hamiltonian/symplectic geometry by making the RNN state dynamics a symplectomorphism, which preserves Legendre duality (information geometry) through time. This yields structure-preserving representations enforced by the latent dynamics, rather than imposed indirectly via the output.

#ReservoirComputing #RepresentationLearning #InformationGeometry #SymplecticGeometry #HamiltonianDynamics #GeometricDeepLearning #DynamicalSystems #PhysicsInformedML

🏆 Congratulations to the 2026 AMS–EMS Mikhail Gordin Prize laureates Simion Filip (University of Chicago) and Vadim Gorin (University of California, Berkeley)!

https://euromathsoc.org/news/2026-ams-ems-mikhail-gordin-prize-awarded-to-simion-filip-and-vadim-gorin-194

#Mathematics #EMS #AMS #Probability #DynamicalSystems

I was thinking about climate tipping points and realized I needed to learn more about the math describing these kinds of phenomena. I found this excellent set of lecture notes, Bifurcations in Biological Dynamics, by André M. de Roos.
https://staff.fnwi.uva.nl/a.m.deroos/projects/BifurcationTheory/index.html

#dynamicalSystems
#tippingPoints
#bifurcations

I was thinking about climate tipping points and realized I needed to learn more about the math describing these kinds of phenomena. I found this excellent set of lecture notes, Bifurcations in Biological Dynamics, by André M. de Roos.
https://staff.fnwi.uva.nl/a.m.deroos/projects/BifurcationTheory/index.html

#dynamicalSystems
#tippingPoints
#bifurcations

I was thinking about climate tipping points and realized I needed to learn more about the math describing these kinds of phenomena. I found this excellent set of lecture notes, Bifurcations in Biological Dynamics, by André M. de Roos.
https://staff.fnwi.uva.nl/a.m.deroos/projects/BifurcationTheory/index.html

#dynamicalSystems
#tippingPoints
#bifurcations

I was thinking about climate tipping points and realized I needed to learn more about the math describing these kinds of phenomena. I found this excellent set of lecture notes, Bifurcations in Biological Dynamics, by André M. de Roos.
https://staff.fnwi.uva.nl/a.m.deroos/projects/BifurcationTheory/index.html

#dynamicalSystems
#tippingPoints
#bifurcations

I was thinking about climate tipping points and realized I needed to learn more about the math describing these kinds of phenomena. I found this excellent set of lecture notes, Bifurcations in Biological Dynamics, by André M. de Roos.
https://staff.fnwi.uva.nl/a.m.deroos/projects/BifurcationTheory/index.html

#dynamicalSystems
#tippingPoints
#bifurcations

On equilateral central configurations in the \(1+4\) -body problem now in Communications in Nonlinear Science and Numerical Simulation from our colleagues E. Barrabés and J.M. Cors and their collaborators M. Álvarez-Ramírez.

Check it out here to learn more:https://www.sciencedirect.com/science/article/pii/S1007570425007749

#dynamicalSystems #appliedMath #MathgoesCelestial

Strange Attractors
https://blog.shashanktomar.com/posts/strange-attractors

Thomas,Aizawa, Simone ,Chen - Lee, Lorenz, Wang - Sun, Dequan Li , Dadras, Rossler, Arneodo, Halvorsen ,Three Scroll ,Chua's Circuit

#vizualization #dynamicalSystems #threejs #simulation #math

Great 8th Barcelona Dynamic Systems Day! Key highlights:
🧠 "Clar que sí. Hi ha sistemes dinàmics dins la nostra ment" by Catalina Vich.
🪐 "Sobre l'estabilitat d'un sistema planetari Sol-Júpiter-Saturn" by Alex Haro.
🏆 Barcelona Dynamical Systems Prize: "Benjamin-Feir instability of Stokes waves" by Massimiliano Berti, Alberto Maspero & Paolo Ventura.

A brilliant day of maths and community. Congrats to the winners and thanks to all!

#DynamicalSystems #Maths #Neuroscience #SolarSystem #Barcelona #8JSD

🔗 https://www.sistemesdinamics.cat/jornades_dir/8_jornada

Great 8th Barcelona Dynamic Systems Day! Key highlights:
🧠 "Clar que sí. Hi ha sistemes dinàmics dins la nostra ment" by Catalina Vich.
🪐 "Sobre l'estabilitat d'un sistema planetari Sol-Júpiter-Saturn" by Alex Haro.
🏆 Barcelona Dynamical Systems Prize: "Benjamin-Feir instability of Stokes waves" by Massimiliano Berti, Alberto Maspero & Paolo Ventura.

A brilliant day of maths and community. Congrats to the winners and thanks to all!

#DynamicalSystems #Maths #Neuroscience #SolarSystem #Barcelona #8JSD

🔗 https://www.sistemesdinamics.cat/jornades_dir/8_jornada

Great 8th Barcelona Dynamic Systems Day! Key highlights:
🧠 "Clar que sí. Hi ha sistemes dinàmics dins la nostra ment" by Catalina Vich.
🪐 "Sobre l'estabilitat d'un sistema planetari Sol-Júpiter-Saturn" by Alex Haro.
🏆 Barcelona Dynamical Systems Prize: "Benjamin-Feir instability of Stokes waves" by Massimiliano Berti, Alberto Maspero & Paolo Ventura.

A brilliant day of maths and community. Congrats to the winners and thanks to all!

#DynamicalSystems #Maths #Neuroscience #SolarSystem #Barcelona #8JSD

🔗 https://www.sistemesdinamics.cat/jornades_dir/8_jornada

Great 8th Barcelona Dynamic Systems Day! Key highlights:
🧠 "Clar que sí. Hi ha sistemes dinàmics dins la nostra ment" by Catalina Vich.
🪐 "Sobre l'estabilitat d'un sistema planetari Sol-Júpiter-Saturn" by Alex Haro.
🏆 Barcelona Dynamical Systems Prize: "Benjamin-Feir instability of Stokes waves" by Massimiliano Berti, Alberto Maspero & Paolo Ventura.

A brilliant day of maths and community. Congrats to the winners and thanks to all!

#DynamicalSystems #Maths #Neuroscience #SolarSystem #Barcelona #8JSD

🔗 https://www.sistemesdinamics.cat/jornades_dir/8_jornada

Great 8th Barcelona Dynamic Systems Day! Key highlights:
🧠 "Clar que sí. Hi ha sistemes dinàmics dins la nostra ment" by Catalina Vich.
🪐 "Sobre l'estabilitat d'un sistema planetari Sol-Júpiter-Saturn" by Alex Haro.
🏆 Barcelona Dynamical Systems Prize: "Benjamin-Feir instability of Stokes waves" by Massimiliano Berti, Alberto Maspero & Paolo Ventura.

A brilliant day of maths and community. Congrats to the winners and thanks to all!

#DynamicalSystems #Maths #Neuroscience #SolarSystem #Barcelona #8JSD

🔗 https://www.sistemesdinamics.cat/jornades_dir/8_jornada

On a Countable Sequence of Homoclinic Orbits Arising Near a Saddle–Center Point, now in Communications in Mathematical Physics from our colleague I. Baldomá and his collaborators M. Guardia and D. E. Pelinovsky.

Check it out here to learn more:
https://link.springer.com/article/10.1007/s00220-025-05381-8

#DynamicalSystems #PeriodicOrbits #SplittingOfSeparatrices