Design of time-delayed connection parameters for inducing amplitude death in high-dimensional oscillator networks

Sugitani, Yoshiki; Konishi, Keiji; Le, Luan Ba; Hara, Naoyuki

doi:10.1063/1.4896318

Cited by 16 publications

(21 citation statements)

References 59 publications

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“…Huddy and Skufca reported that delay connections can induce the stabilization of an operating point in coupled dc bus systems [22], This stabilization is referred to as time-delay-induced amplitude death, which is a well-known phenomenon in the field of nonlinear science [31][32][33][34]. The stability of amplitude death is closely related to that of our decentralized delayed-feedback controller (14).…”

Section: Discussionmentioning

confidence: 93%

Dynamics of dc bus networks and their stabilization by decentralized delayed feedback

2015

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The present paper deals with the dynamics of bus networks, which consist of several identical dc bus systems connected by resistors. It is analytically guaranteed that the stability of a stand-alone dc bus system is equivalent to that of the networks, independent of the number of bus systems and the network topology. In addition, we show that a decentralized delayed-feedback control can stabilize an unstable operating point embedded within the networks. Moreover, this stabilization does not depend on the number of bus systems or the network topology. A systematic procedure for designing the controller is presented. Finally, the validity of the analytical results is confirmed through numerical examples.

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Section: Discussionmentioning

confidence: 93%

Dynamics of dc bus networks and their stabilization by decentralized delayed feedback

2015

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“…with a diagonal transformation matrix T [22,23,28,29]. The transformation δx(n) = T ξ(n) allows us to obtain…”

Section: Stability Analysismentioning

confidence: 99%

“…. , N) of asymmetric matrix M := I N − C are always within the range ρ q ∈ [0, 2] [22,23,28,29], i.e.,…”

Section: Delay-coupled Bernoulli Map Networkmentioning

confidence: 99%

“…Based on such studies, a systematic design procedure for the connection to induce a desired phenomenon in coupled oscillators has created considerable interest in recent years. As a result, a design problem for inducing the desired phase dynamics in coupled oscillators has been proposed [17][18][19][20], and design problems for inducing the amplitude death phenomenon have been solved using a robust control theory [21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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Delay-independent design for chaotic synchronization in delay-coupled Bernoulli map networks

Sugitani¹,

Watanabe

Konishi

et al. 2017

NOLTA

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Abstract:The present paper considers chaotic synchronization in a network consisting of Bernoulli maps with a time-delay connection. We demonstrate that a connection strength and a map parameter at which chaotic synchronization occurs can be systematically designed, even for cases in which the connection delay, the number of maps, and the detailed topology information are unknown. The primary advantage of the proposed design is that the designed connection strength and map parameter are valid for any connection delay. This result is due to the fact that the stability of the synchronized state is the same as that of a timeinvariant linear system having both an uncertain dimension and an uncertain parameter. For such a linear system, it is quite difficult to obtain the necessary and sufficient condition of the stability. However, a simple sufficient condition enables us to provide the design. The analytical results are confirmed through numerical examples.

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“…Pyragas (Pyragas, 1992) (Nakajima, 1997) (amplitude death) (Konishi, 2005) A (Sugitani et al, 2014) (2) τ(t) …”

Section: N   ẋ I (T) = Ax I (T) + F (X I (T)) + G(x I (T))u I (T)mentioning

confidence: 99%

Synchronization and stabilization of coupled unstable systems with delayed couplings

Ryono¹,

Oguchi²

2017

Transactions of the JSME (In Japanese)

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This paper considers the simultaneous stabilization problem for multiple identical unstable systems using network synchronization. In particular, we attempt to design a coupling such that all systems in networks are synchronized, and each system is stabilized at the equilibrium point. The proposed coupling consists of a linear combination of the projective synchronization errors with a constant scaling factor and the delayed values. To realize the simultaneous stabilization based on synchronization, we consider the local stability of both the equilibrium point of a system in the networks and the synchronization errors between the system and others. From the stability analysis, we show that synchronization for mutual-coupled systems with the proposed coupling can lead to the simultaneous stabilization of This result also supports the usefulness of the proposed scheme.

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Design of time-delayed connection parameters for inducing amplitude death in high-dimensional oscillator networks

Cited by 16 publications

References 59 publications

Dynamics of dc bus networks and their stabilization by decentralized delayed feedback

Dynamics of dc bus networks and their stabilization by decentralized delayed feedback

Delay-independent design for chaotic synchronization in delay-coupled Bernoulli map networks

Synchronization and stabilization of coupled unstable systems with delayed couplings

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