An Introduction to Emergence Dynamics in Complex Systems

Zheng, Zhigang

doi:10.1007/978-981-15-9297-3_4

Cited by 8 publications

(3 citation statements)

References 92 publications

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“…Let us theoretically analyze the stability of the synchronous state of system (1). A typical synchronous state is the in-phase state (IPS) defined as…”

Section: Stability Of the Synchronous Statementioning

confidence: 99%

“…Self organization and collective behaviors can be extensively observed in complex systems composed of large numbers of interacting units. [1] Synchronization is a collective emergent behavior ubiquitously observed in many systems, [2,3] such as cardiac pacemaker cells, [4] fireflies, [5] biochemical systems, [6] and neuronal networks. [7] Furthermore, synchronization also has practical significance in aspects of modern life, such as the functioning of power grids which is based on the synchronization of power generators.…”

Section: Introductionmentioning

confidence: 99%

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Stability and multistability of synchronization in networks of coupled phase oscillators

et al. 2023

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Coupled phase oscillators usually achieve synchronization as the coupling strength among oscillators is increased beyond a critical value. The stability of synchronous state remains an open issue. In this paper, we study the stability of the synchronous state in coupled phase oscillators. It is found that numerical integration of differential equations of coupled phase oscillators with a finite time step may induce desynchronization at strong couplings. The mechanism behind this instability is that numerical accumulated errors in simulations may trigger the loss of stability of the synchronous state. Desynchronization critical couplings are found to increase and diverge as a power law with decreasing the integral time step. Theoretical analysis supports the local stability of synchronized state. Globally the emergence of synchronous state depends on initial conditions. Other metastable ordered states such as twisted states can coexist with the synchronous mode. These twisted states keep locally stable on a sparse network but lose their stability when the network becomes dense.

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“…Let us theoretically analyze the stability of the synchronous state of system (1). A typical synchronous state is the in-phase state (IPS) defined as…”

Section: Stability Of the Synchronous Statementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability and multistability of synchronization in networks of coupled phase oscillators

et al. 2023

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“…[1] A systematic exploration of the emergence of complex systems is the core mission of complexity science. [2] Synchronization implies the rhythmic coordination between two or more elements, which has been ubiquitously observed and relevant in many processes, [3] ranging from groups of cardiac pacemaker cells, [4] coupled metronomes, [5] large groups of fireflies, [6,7] biochemical oscillators, [8] oscillating neutrinos, [9] power grids [10] and neuronal synchronization. [11] Further studies have been extended to chaotic systems, and complete synchronization, [12,13] generalized synchronization, [14,15] lag synchronization, [16] and even measure synchronization [17] have been exhaustively explored.…”

Section: Introductionmentioning

confidence: 99%

Synchronization–desynchronization transitions in networks of circle maps with sinusoidal coupling

2023

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Coupled phase oscillators are adopted as powerful platforms in studying synchrony behaviors emerged in various systems with rhythmic dynamics. Much attention had been focused on coupled time-continuous oscillators described by differential equations. In this paper, we study the synchronization dynamics of networks of coupled circle maps as the discrete version of the Kuramoto model. Despite of its simplicity in mathematical form, it is found that discreteness may induce many interesting synchronization behaviors. Multiple synchronization and desynchronization transitions of both phases and frequencies are found with varying the coupling among circle-map oscillators. The mechanisms of these transitions are interpreted in terms of the mean-field approach, where collective bifurcation cascades are revealed for coupled circle-map oscillators.

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Fractalization of Chaos and Complexity: Proposition of a New Method in the Study of Complex Systems

Serpa

Forouharfar

2021

Chaos, Complexity and Leadership 2020

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An Introduction to Emergence Dynamics in Complex Systems

Cited by 8 publications

References 92 publications

Stability and multistability of synchronization in networks of coupled phase oscillators

Stability and multistability of synchronization in networks of coupled phase oscillators

Synchronization–desynchronization transitions in networks of circle maps with sinusoidal coupling

Fractalization of Chaos and Complexity: Proposition of a New Method in the Study of Complex Systems

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