Extreme multistability in a chemical model system

Ngonghala, Calistus N.; Feudel, Ulrike; Showalter, Kenneth

doi:10.1103/physreve.83.056206

Cited by 108 publications

(43 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…More importantly, we emphasize that Ngonghala et al [4] have shown that a necessary condition for the emergence of extreme multistability is the existence of a conserved quantity C. Since the value of this conserved quantity can take any real number, the dynamics finally takes place on a manifold characterized by this conserved quantity. In turn, this corresponds to a foliation of the state space into infinitely many such manifolds each of them containing at least one attractor.…”

mentioning

confidence: 73%

See 1 more Smart Citation

Reply to “Comment on ‘How to obtain extreme multistability in coupled dynamical systems’ ”

et al. 2014

View full text Add to dashboard Cite

In this Reply we answer the two major issues raised by the Comment. First, we point out that the idea of constructing extreme multistability in simple dynamical systems is not new and has been demonstrated previously by other authors. Furthermore, we emphasize the importance of the concept of a conserved quantity and its consequences for the dynamics, which applies to all the examples in the Comment. Second, we show that the design of controllers to achieve extreme multistability in coupled systems is as general as described in Phys. Rev. E 85, 035202(R) (2012) by providing two examples which do not lead to a master-slave dynamics.

show abstract

mentioning

confidence: 73%

“…(5) in the Comment [1]. The same mathematical form can also occur in coupled systems, as discussed in the first coupled autocatalator system analyzed in [4].…”

mentioning

confidence: 81%

Reply to “Comment on ‘How to obtain extreme multistability in coupled dynamical systems’ ”

et al. 2014

View full text Add to dashboard Cite

show abstract

“…It should be pointed out that an infinite number of equilibria could be obtained in the jerk circuit under consideration via replacing the semiconductor diode (the nonlinear component) with a flux controlled memristor [14,35]. Such types of systems are more suited to develop the phenomenon of extreme multistability [11,36,37] involving the coexistence of an infinite number of attractors for the same parameter setting, depending only on the choice of initial conditions. Research along this line is under consideration and the results will be the material of an upcoming publication.…”

Section: Discussionmentioning

confidence: 99%

Asymmetric Double Strange Attractors in a Simple Autonomous Jerk Circuit

et al. 2018

View full text Add to dashboard Cite

The dynamics of a simple autonomous jerk circuit previously introduced by Sprott in 2011 are investigated. In this paper, the model is described by a three-time continuous dimensional autonomous system with an exponential nonlinearity. Using standard nonlinear techniques such as time series, bifurcation diagrams, Lyapunov exponent plots, and Poincaré sections, the dynamics of the system are characterized with respect to its parameters. Period-doubling bifurcations, periodic windows, and coexisting bifurcations are reported. As a major result of this work, it is found that the system experiences the unusual phenomenon of asymmetric bistability marked by the presence of two different attractors (e.g., screw-like Shilnikov attractor with a spiralling-like Feigenbaum attractor) for the same parameters setting, depending solely on the choice of initial states. Among few cases of lower dimensional systems capable of such type of behavior reported to date (e.g., Colpitts oscillator, Newton-Leipnik system, and hyperchaotic oscillator with gyrators), the jerk circuit/system considered in this work represents the simplest prototype. Results of theoretical analysis are perfectly reproduced by laboratory experimental measurements.

show abstract

“…7,8 While in the aforementioned coupled systems the number of coexisting attractors is finite, one can also find an infinite number of attractors when two arbitrary, but identical systems are coupled in a specific way. 9 This particular kind of multistability has been termed uncertain destination dynamics 10 or extreme multistability, 11 and it is related to the emergence of a conserved quantity in the long-term limit. The third class of multistable systems is delayed feedback- systems, where additional attractors appear depending on the variation of the delay.…”

Section: A Classes and Properties Of Multistable Systemsmentioning

confidence: 99%

Multistability and tipping: From mathematics and physics to climate and brain—Minireview and preface to the focus issue

Feudel

Pisarchik

Showalter

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

116

View full text Add to dashboard Cite

Multistability refers to the coexistence of different stable states in nonlinear dynamical systems. This phenomenon has been observed in laboratory experiments and in nature. In this introduction, we briefly introduce the classes of dynamical systems in which this phenomenon has been found and discuss the extension to new system classes. Furthermore, we introduce the concept of critical transitions and discuss approaches to distinguish them according to their characteristics. Finally, we present some specific applications in physics, neuroscience, biology, ecology, and climate science.

show abstract

Extreme multistability in a chemical model system

Cited by 108 publications

References 39 publications

Reply to “Comment on ‘How to obtain extreme multistability in coupled dynamical systems’ ”

Reply to “Comment on ‘How to obtain extreme multistability in coupled dynamical systems’ ”

Asymmetric Double Strange Attractors in a Simple Autonomous Jerk Circuit

Multistability and tipping: From mathematics and physics to climate and brain—Minireview and preface to the focus issue

Contact Info

Product

Resources

About