Multistablity, bistability and bubbles phenomena in a periodically forced ethanol fermentor

Abashar, M.E.E.; Elnashaie, S.S.E.H.

doi:10.1016/j.ces.2011.08.040

Cited by 15 publications

(12 citation statements)

References 52 publications

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“…Different ways of synchronization phenomena have been outlined, but one of the most remarkable is forced synchronization, where two or more systems are constrained by an external signal. This type of interconnection has unveiled several applications in many scientific areas, as it is in chemistry [1][2][3], robotics [4] and geophysics [5], in which an external continuous or periodic signal is received by the forced systems.…”

Section: Introductionmentioning

confidence: 99%

Preservation of a two-wing Lorenz-like attractor with stable equilibria

Ontañón-García

Campos-Cantón

2013

Journal of the Franklin Institute

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Section: Introductionmentioning

confidence: 99%

Preservation of a two-wing Lorenz-like attractor with stable equilibria

Ontañón-García

Campos-Cantón

2013

Journal of the Franklin Institute

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“…Bifurcation analysis not only investigates the unforced system but also estimates the dynamic complexities when periodic forcing is introduced. Classic methodical tools include codimension-1 bifurcations of limit cycles and stroboscopic Poincare maps [43], due to chaos during period-doubling and Neimark-Sacker bifurcations being frequently evident in the CSTRs.…”

Section: Introductionmentioning

confidence: 99%

A cubic autocatalator chemical reaction model with limit cycle analysis and consistency preserving discretization

Din¹,

Shabir²

2021

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This article deals with the study of some qualitative properties of a cubic autocatalator chemical reaction model. Particularly, we obtain a dynamically consistent cubic autocatalator discrete-time model by applying a nonstandard difference scheme. Analysis of the existence of equilibria and their stability is carried out. It is proved that a continuous system undergoes the Hopf bifurcation at its interior equilibrium, whereas the discrete-time version undergoes Neimark-Sacker bifurcation at its interior fixed point. Moreover, numerical simulation is provided to strengthen our theoretical discussion.

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“…Bifurcation analysis studies dynamic complexities by using only steady-state information of the CSTRs, and can be used not only to analyze the unforced system, but also to evaluate the dynamic changes when periodic forcing is introduced. Typical analytical tools include stroboscopic Poincaré maps and codimension-1 bifurcations of limit cycles [20], with the route to chaos through period doubling (PD) and Neimark-Sacker (NS) bifurcations being commonly observable in the CSTRs.…”

Section: Introductionmentioning

confidence: 99%

Study on the Nonlinear Dynamics of the Continuous Stirred Tank Reactors

et al. 2020

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Chemical processes often exhibit nonlinear dynamics and tend to generate complex state trajectories, which present challenging operational problems due to complexities such as output multiplicity, oscillation, and even chaos. For this reason, a complete knowledge of the static and dynamic nature of these behaviors is required to understand, to operate, to control, and to optimize continuous stirred tank reactors (CSTRs). Through nonlinear analysis, the possibility of output multiplicity, self-sustained oscillation, and torus dynamics are studied in this paper. Specifically, output multiplicity is investigated in a case-by-case basis, and related operation and control strategies are discussed. Bifurcation analysis to identify different dynamic behaviors of a CSTR is also implemented, where operational parameters are identified to obtain self-oscillatory dynamics and possible unsteady-state operation strategy through designing the CSTR as self-sustained periodic. Finally, a discussion on codimension-1 bifurcations of limits cycles is also provided for the exploration of periodic forcing on self-oscillators. Through this synergistic study on the CSTRs, possible output multiplicity, oscillatory, and chaotic dynamics facilitates the implementation of novel operation/control strategies for the process industry.

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Multistablity, bistability and bubbles phenomena in a periodically forced ethanol fermentor

Cited by 15 publications

References 52 publications

Preservation of a two-wing Lorenz-like attractor with stable equilibria

Preservation of a two-wing Lorenz-like attractor with stable equilibria

A cubic autocatalator chemical reaction model with limit cycle analysis and consistency preserving discretization

Study on the Nonlinear Dynamics of the Continuous Stirred Tank Reactors

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