Complex dynamics in the two spring-block model for earthquakes with fractional viscous damping

Tanekou, G. B.; Fogang, C. F.; Pelap, F. B.; Kengne, Romanic; Fozin, T. Fonzin; Nbendjo, B. R. Nana

doi:10.1140/epjp/s13360-020-00558-7

Cited by 8 publications

(3 citation statements)

References 66 publications

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“…Rather than requiring phase space reconstruction, which is necessary to apply standard Lyapunov exponent methods in the analysis of discrete data, the test works directly with the time series and does not involve any preprocessing of the data [53]. A thorough description and the use of the method can be found in [53][54][55][56].…”

Section: Discussionmentioning

confidence: 99%

Chimera states in a neuronal network under the action of an electric field

Simo,

Njougouo,

Aristides

et al. 2021

Preprint

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The phenomenon of the chimera state symbolizes the coexistence of coherent and incoherent sections of a given population. This phenomenon identified in several physical and biological systems presents several variants, including the multichimera states and the traveling chimera state. Here, we numerically study the influence of a weak external electric field on the dynamics of a network of Hindmarsh-Rose (HR) neurons coupled locally by an electrical interaction and nonlocally by a chemical one. We first focus on the phenomena of traveling chimera states and multicluster oscillating breathers that appear in the electric field's absence. Then in the field's presence, we highlight the presence of a chimera state, a multichimera state, an alternating chimera state and a multicluster traveling chimera.

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Section: Discussionmentioning

confidence: 99%

Chimera states in a neuronal network under the action of an electric field

Simo,

Njougouo,

Aristides

et al. 2021

Preprint

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“…It can be seen that when estimating the state at time k , it is necessary to calculate the state of the past k − 1 times, which increases the complexity of the algorithm greatly. When estimating the state of time k , only the influence from time k − L to time k is considered by introducing the short memory principle 41 . It is worth noting that when the state time k does not exceed the memory length, the influence of past k − 1 states is considered.…”

Section: Theoretical Analysismentioning

confidence: 99%

Improved fractional‐order hysteresis‐equivalent circuit modeling for the online adaptive high‐precision state of charge prediction of urban‐electric‐bus lithium‐ion batteries

Zeng,

Wang,

Cao

et al. 2023

Circuit Theory & Apps

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SummaryAccurate state of charge (SOC) estimation is based on a precise battery model and is the focus of the battery management system (BMS). First, based on the second‐order RC equivalent circuit model and Grunwald–Letnikov (G‐L) definition, the high‐precision fractional‐order hysteresis‐equivalent circuit model (FH‐ECM) is established considering the open‐circuit voltage hysteresis effect. Then, the global parameters of the battery model are identified using a particle swarm algorithm optimized by the genetic algorithm (GA‐PSO). Third, a fractional‐order adaptive unscented Kalman filter (FOAUKF) algorithm is derived to estimate the SOC of lithium‐ion batteries. Finally, the feasibility of the model and algorithm is verified under complex working conditions. Under the dynamic stress test (DST) condition, the accuracy of model terminal voltage has been improved by 37.83%, and the error of SOC estimation has been reduced by 11.28%. Under Beijing bus dynamic stress test (BBDST) condition, the model terminal voltage accuracy has been improved by 51.44%, and the SOC estimation error has been reduced by 35.71%. The experimental results fully confirm the accuracy of the fractional‐order hysteresis‐equivalent circuit modeling method.

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“…The aim of studying the chaotic nonlinear dynamics of jerk systems is to understand the complex behavior that arises in systems that exhibit sudden changes in acceleration [9]. Aside from jerk systems themselves, the study of such nonlinear systems can reveal information on the behavior of physical systems such as earthquakes [10,11], satellites [12,13], and biological systems [14][15][16]. The chaotic behavior of jerk systems can also be applied in engineering applications such as control systems, robotics, and signal processing [17,18].…”

Section: Introductionmentioning

confidence: 99%

Energy function and complex dynamics from a jerk system

Yu,

Njitacke,

Jiang

et al. 2023

Phys. Scr.

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Jerk, as a mathematical concept, is used in mechanics to describe the rate of change of acceleration and plays a crucial role in the design of control systems for machines and vehicles. Therefore, it is important to master the various states and the energy released during the change of acceleration. This is why a new simple jerk function introduced afterward, energy released, is derived from a Hamilton function using the Helmholtz theorem. The condition of having a stable or unstable rate of change of acceleration is established using Hopf bifurcation theory. Some two-parameter stability charts are then computed for a suitable selection region of the study. Using some nonlinear analysis metrics, in the unstable region of the study, the occurrence of phenomena is found, such as reverse period doubling bifurcation, antimonotonicity, and hysteresis involving the coexistence of the states in the considered jerk system. An electronic circuit is built and used to implement the mathematical expression of the jerk equation and validate the result of the theoretical investigation.

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Complex dynamics in the two spring-block model for earthquakes with fractional viscous damping

Cited by 8 publications

References 66 publications

Chimera states in a neuronal network under the action of an electric field

Chimera states in a neuronal network under the action of an electric field

Improved fractional‐order hysteresis‐equivalent circuit modeling for the online adaptive high‐precision state of charge prediction of urban‐electric‐bus lithium‐ion batteries

Energy function and complex dynamics from a jerk system

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