Transient behavior is thought to play an integral role in brain functionality. Numerical simulations of the firing activity of diffusively coupled, excitable Morris-Lecar neurons reveal transient spatiotemporal chaos in the parameter regime below the saddle-node on invariant circle bifurcation point. The neighborhood of the chaotic saddle is reached through perturbations of the rest state, in which few initially active neurons at an effective spatial distance can initiate spatiotemporal chaos. The system escapes from the neighborhood of the chaotic saddle to either the rest state or to a state of pulse propagation. The lifetime of the chaotic transients is manipulated in a statistical sense through a singular application of a synchronous perturbation to a group of neurons.
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http://dx.doi.org/10.1063/1.4866974 | DOI Listing |
Neural Netw
January 2025
Defense Innovation Institute, Chinese Academy of Military Science, Beijing 100071, China; Intelligent Game and Decision Laboratory, China.
The Physics-informed Neural Network (PINN) has been a popular method for solving partial differential equations (PDEs) due to its flexibility. However, PINN still faces challenges in characterizing spatio-temporal correlations when solving parametric PDEs due to network limitations. To address this issue, we propose a Physics-Informed Neural Implicit Flow (PINIF) framework, which enables a meshless low-rank representation of the parametric spatio-temporal field based on the expressiveness of the Neural Implicit Flow (NIF), enabling a meshless low-rank representation.
View Article and Find Full Text PDFBull Math Biol
January 2025
Department of Mathematics, Vivekananda College, Kolkata, West Bengal, 700063, India.
The extinction of species is a major threat to the biodiversity. Allee effects are strongly linked to population extinction vulnerability. Emerging ecological evidence from numerous ecosystems reveals that the Allee effect, which is brought on by two or more processes, can work on a single species concurrently.
View Article and Find Full Text PDFChaos
January 2025
School of Mathematical & Computer Sciences, Heriot-Watt University, EH14 4AS Edinburgh, United Kingdom.
Time-evolving graphs arise frequently when modeling complex dynamical systems such as social networks, traffic flow, and biological processes. Developing techniques to identify and analyze communities in these time-varying graph structures is an important challenge. In this work, we generalize existing spectral clustering algorithms from static to dynamic graphs using canonical correlation analysis to capture the temporal evolution of clusters.
View Article and Find Full Text PDFChaos
January 2025
Department of Physics, Tohoku University, Sendai 980-8578, Japan.
An Ott-Antonsen reduced M-population of Kuramoto-Sakaguchi oscillators is investigated, focusing on the influence of the phase-lag parameter α on the collective dynamics. For oscillator populations coupled on a ring, we obtained a wide variety of spatiotemporal patterns, including coherent states, traveling waves, partially synchronized states, modulated states, and incoherent states. Back-and-forth transitions between these states are found, which suggest metastability.
View Article and Find Full Text PDFChaos
December 2024
Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India.
This study expands traditional reaction-diffusion models by incorporating hyperbolic dynamics to explore the effects of inertial delays on pattern formation. The kinetic system considers a harvested predator-prey model where predator and prey populations gather in herds. Diffusion and inertial effects are subsequently introduced.
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