Phase transitions in networks of chaotic elements with short and long range interactions

Losson, Jérôme; Milton, John; Mackey, Michael C.

doi:10.1016/0167-2789(94)00203-3

Cited by 20 publications

(4 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…2(a) and 2(b). A similar behavior has been observed in the context of the Belousov-Zhabotinsky reaction and has been studied in terms of asymmetric bimodal maps [30,31]. Following Ref.…”

Section: Resultssupporting

confidence: 72%

Influence of time-delayed feedback in the firing pattern of thermally sensitive neurons

Sainz-Trapága

Masoller

Braun³

et al. 2004

Phys. Rev. E

View full text Add to dashboard Cite

We explore the dynamics of a Hodgkin-Huxley-type model for thermally sensitive neurons that exhibit intrinsic oscillatory activity. The model is modified to include a feedback loop that is represented by two parameters: the synaptic strength and the transmission delay time. We analyze the dynamics of the neuron depending on the temperature, the synaptic strength, and the delay time. We find parameter regions where the effect of the recurrent connexion is excitatory, inducing spikes or trains of spikes, and regions where it is inhibitory, reducing or eliminating completely the spiking behavior. We characterize the complex interplay of the intrinsic dynamics of the neuron with the recurrent feedback input and a noisy input.

show abstract

“…2(a) and 2(b). A similar behavior has been observed in the context of the Belousov-Zhabotinsky reaction and has been studied in terms of asymmetric bimodal maps [30,31]. Following Ref.…”

Section: Resultssupporting

confidence: 72%

Influence of time-delayed feedback in the firing pattern of thermally sensitive neurons

Sainz-Trapága

Masoller

Braun³

et al. 2004

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…that a phase of matter is. Similar behavior has been studied in the non-linear dynamics community as either "subharmonic entrainment" or "asymptotic periodicity" [29][30][31][32][33]; for a discussion of how this earlier work differs from results in the quantum many-body context, we refer the reader to [7,34,35].…”

Section: Introductionmentioning

confidence: 82%

An absolutely stable open time crystal

Zhuang¹,

Machado²,

Yao³

et al. 2021

Preprint

View full text Add to dashboard Cite

We show that locally-interacting, periodically-driven (Floquet) Hamiltonian dynamics coupled to a Langevin bath support finite-temperature discrete time crystals with an infinite auto-correlation time. The time crystalline order is stable to arbitrary perturbations, including those that break the time translation symmetry of the underlying drive. Our approach utilizes a general mapping from probabilistic cellular automata (PCA) to open classical Floquet systems. Applying this mapping to a variant of the Toom cellular automata, which we dub the "π-Toom PCA", leads to a 2D Floquet Hamiltonian with a finite-temperature period-doubling phase transition. We provide numerical evidence for the existence of this transition, and analyze the statistics of the finite temperature fluctuations. Finally, we discuss how general results from the field of probabilistic cellular automata imply the existence of discrete time crystals in all dimensions, D ≥ 1.

show abstract

“…Most published results concerning the stabilization and synchronization of CMLs have been obtained by numerical studies for various parameters due to different coupling, different neighborhoods, and different updating. A number of theoretical approaches have been developed to describe these numerical results analytically [16,17,18,19,20]. In this contribution we present, for the first time, a comprehensive stability analysis of CMLs at locally unstable fixed points, which allows us to understand corresponding numerical results theoretically.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of coupled map lattices at locally unstable fixed points

2005

View full text Add to dashboard Cite

Numerical simulations of coupled map lattices (CMLs) and other complex model systems show an enormous phenomenological variety that is difficult to classify and understand. It is therefore desirable to establish analytical tools for exploring fundamental features of CMLs, such as their stability properties. Since CMLs can be considered as graphs, we apply methods of spectral graph theory to analyze their stability at locally unstable fixed points for different updating rules, different coupling scenarios, and different types of neighborhoods. Numerical studies are found to be in excellent agreement with our theoretical results.

show abstract

Phase transitions in networks of chaotic elements with short and long range interactions

Cited by 20 publications

References 28 publications

Influence of time-delayed feedback in the firing pattern of thermally sensitive neurons

Influence of time-delayed feedback in the firing pattern of thermally sensitive neurons

An absolutely stable open time crystal

Stability analysis of coupled map lattices at locally unstable fixed points

Contact Info

Product

Resources

About