Zobrazeno 1 - 10
of 200
pro vyhledávání: '"Bick Christian"'
Autor:
Bick Christian, Hüser Dorothee
Publikováno v:
BIO Web of Conferences, Vol 129, p 04046 (2024)
Externí odkaz:
https://doaj.org/article/cf73ab6dd6364b778b9498379ac5cd94
Complex contagion models that involve contagion along higher-order structures, such as simplicial complexes and hypergraphs, yield new classes of mean-field models. Interestingly, the differential equations arising from many such models often exhibit
Externí odkaz:
http://arxiv.org/abs/2410.15330
Autor:
Bick, Christian, Lohse, Alexander
Homoclinic and heteroclinic connections can form cycles and networks in phase space, which organize the global phenomena in dynamical systems. On the one hand, stability notions for (omni)cycles give insight into how many initial conditions approach
Externí odkaz:
http://arxiv.org/abs/2410.11383
This paper concerns discrete-time occupancy processes on a finite graph. Our results can be formulated in two theorems, which are stated for vertex processes, but also applied to edge process (e.g., dynamic random graphs). The first theorem shows tha
Externí odkaz:
http://arxiv.org/abs/2410.06807
We consider synchrony patterns in coupled phase oscillator networks that correspond to invariant tori. For specific nongeneric coupling, these tori are equilibria relative to a continuous symmetry action. We analyze how the invariant tori deform unde
Externí odkaz:
http://arxiv.org/abs/2408.02119
Autor:
Ashwin, Peter, Bick, Christian
Frequency desynchronized attractors cannot appear in identically coupled symmetric phase oscillators because "overtaking" of phases cannot occur. This restriction no longer applies for more general identically coupled oscillators. Hence, it is intere
Externí odkaz:
http://arxiv.org/abs/2407.12524
Coupled oscillators with time-delayed network interactions are critical to understand synchronization phenomena in many physical systems. Phase reductions to finite-dimensional phase oscillator networks allow for their explicit analysis. However, fir
Externí odkaz:
http://arxiv.org/abs/2404.11340
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling, these trans
Externí odkaz:
http://arxiv.org/abs/2402.16471
Publikováno v:
Journal of Physics: Complexity, 5:025026, 2024
Synchronization is an essential collective phenomenon in networks of interacting oscillators. Twisted states are rotating wave solutions in ring networks where the oscillator phases wrap around the circle in a linear fashion. Here, we analyze Hopf bi
Externí odkaz:
http://arxiv.org/abs/2310.15698
Autor:
Bick, Christian, von der Gracht, Sören
Publikováno v:
Journal of Complex Networks (2024) 2
Heteroclinic structures organize global features of dynamical systems. We analyze whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We f
Externí odkaz:
http://arxiv.org/abs/2309.02006