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Article ; Online: Coexistence of three heteroclinic cycles and chaos analyses for a class of 3D piecewise affine systems.

Wang, Fanrui / Wei, Zhouchao / Zhang, Wei / Moroz, Irene

2023 Volume 33, Issue 2, Page(s) 23108

Abstract: Our objective is to investigate the innovative dynamics of piecewise smooth systems with multiple discontinuous switching manifolds. This paper establishes the coexistence of heteroclinic cycles in a class of 3D piecewise affine systems with three ... ...

Abstract	Our objective is to investigate the innovative dynamics of piecewise smooth systems with multiple discontinuous switching manifolds. This paper establishes the coexistence of heteroclinic cycles in a class of 3D piecewise affine systems with three switching manifolds through rigorous mathematical analysis. By constructing suitable Poincaré maps adjacent to heteroclinic cycles, we demonstrate the occurrence of two distinct types of horseshoes and show the conditions for the presence of chaotic invariant sets. A family of attractors that satisfy the criteria are presented using this technique. It is shown that the outcomes of numerical simulation accurately reflect those of our theoretical results.
Language	English
Publishing date	2023-03-01
Publishing country	United States
Document type	Journal Article
ZDB-ID	1472677-4
ISSN	1089-7682 ; 1054-1500
ISSN (online)	1089-7682
ISSN	1054-1500
DOI	10.1063/5.0132018
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Melnikov-type method for a class of planar hybrid piecewise-smooth systems with impulsive effect and noise excitation: Heteroclinic orbits.

Wei, Zhouchao / Li, Yuxi / Moroz, Irene / Zhang, Wei

Chaos (Woodbury, N.Y.)

2022 Volume 32, Issue 10, Page(s) 103127

Abstract: The classical Melnikov method for heteroclinic orbits is extended theoretically to a class of hybrid piecewise-smooth systems with impulsive effect and noise excitation. We assume that the unperturbed system is a piecewise Hamiltonian system with a pair ... ...

Abstract	The classical Melnikov method for heteroclinic orbits is extended theoretically to a class of hybrid piecewise-smooth systems with impulsive effect and noise excitation. We assume that the unperturbed system is a piecewise Hamiltonian system with a pair of heteroclinic orbits. The heteroclinic orbit transversally jumps across the first switching manifold by an impulsive effect and crosses the second switching manifold continuously. In effect, the trajectory of the corresponding perturbed system crosses the second switching manifold by applying the reset map describing the impact rule instantaneously. The random Melnikov process of such systems is then derived by measuring the distance of perturbed stable and unstable manifolds, and the criteria for the onset of chaos with or without noise excitation is established. In this derivation process, we overcome the difficulty that the derivation method of the corresponding homoclinic case cannot be directly used due to the difference between the symmetry of the homoclinic orbit and the asymmetry of the heteroclinic orbit. Finally, we investigate the complicated dynamics of a particular piecewise-smooth system with and without noise excitation under the reset maps, impulsive effect, and non-autonomous periodic and damping perturbations by this new extended method and numerical simulations. The numerical results verify the correctness of the theoretical results and demonstrate that this extended method is simple and effective for studying the dynamics of such systems.
Language	English
Publishing date	2022-08-10
Publishing country	United States
Document type	Journal Article
ZDB-ID	1472677-4
ISSN	1089-7682 ; 1054-1500
ISSN (online)	1089-7682
ISSN	1054-1500
DOI	10.1063/5.0106073
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Article ; Online: Noise induced suppression of spiral waves in a hybrid FitzHugh-Nagumo neuron with discontinuous resetting.

Rajagopal, Karthikeyan / Jafari, Sajad / Moroz, Irene / Karthikeyan, Anitha / Srinivasan, Ashokkumar

Chaos (Woodbury, N.Y.)

2021 Volume 31, Issue 7, Page(s) 73117

Abstract: A modified FitzHugh-Nagumo neuron model with sigmoid function-based recovery variable is considered with electromagnetic flux coupling. The dynamical properties of the proposed neuron model are investigated, and as the excitation current becomes larger, ... ...

Abstract	A modified FitzHugh-Nagumo neuron model with sigmoid function-based recovery variable is considered with electromagnetic flux coupling. The dynamical properties of the proposed neuron model are investigated, and as the excitation current becomes larger, the number of fixed points decreases to one. The bifurcation plots are investigated to show the chaotic and periodic regimes for various values of excitation current and parameters. A N×N network of the neuron model is constructed to study the wave propagation and wave re-entry phenomena. Investigations are conducted to show that for larger flux coupling values, the spiral waves are suppressed, but for such values of the flux coupling, the individual nodes are driven into periodic regimes. By introducing Gaussian noise as an additional current term, we showed that when noise is introduced for the entire simulation time, the dynamics of the nodes are largely altered while the noise exposure for 200-time units will not alter the dynamics of the nodes completely.
MeSH term(s)	Computer Simulation ; Neurons
Language	English
Publishing date	2021-08-02
Publishing country	United States
Document type	Journal Article
ZDB-ID	1472677-4
ISSN	1089-7682 ; 1054-1500
ISSN (online)	1089-7682
ISSN	1054-1500
DOI	10.1063/5.0059175
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Article ; Online: Local and network behavior of bistable vibrational energy harvesters considering periodic and quasiperiodic excitations.

Rajagopal, Karthikeyan / Ramesh, Arthanari / Moroz, Irene / Duraisamy, Prakash / Karthikeyan, Anitha

Chaos (Woodbury, N.Y.)

2021 Volume 31, Issue 6, Page(s) 63111

Abstract: Vibrational energy harvesters can exhibit complex nonlinear behavior when exposed to external excitations. Depending on the number of stable equilibriums, the energy harvesters are defined and analyzed. In this work, we focus on the bistable energy ... ...

Abstract	Vibrational energy harvesters can exhibit complex nonlinear behavior when exposed to external excitations. Depending on the number of stable equilibriums, the energy harvesters are defined and analyzed. In this work, we focus on the bistable energy harvester with two energy wells. Though there have been earlier discussions on such harvesters, all these works focus on periodic excitations. Hence, we are focusing our analysis on both periodic and quasiperiodic forced bistable energy harvesters. Various dynamical properties are explored, and the bifurcation plots of the periodically excited harvester show coexisting hidden attractors. To investigate the collective behavior of the harvesters, we mathematically constructed a two-dimensional lattice array of the harvesters. A non-local coupling is considered, and we could show the emergence of chimeras in the network. As discussed in the literature, energy harvesters are efficient if the chaotic regimes can be suppressed and hence we focus our discussion toward synchronizing the nodes in the network when they are not in their chaotic regimes. We could successfully define the conditions to achieve complete synchronization in both periodic and quasiperiodically excited harvesters.
Language	English
Publishing date	2021-06-08
Publishing country	United States
Document type	Journal Article
ZDB-ID	1472677-4
ISSN	1089-7682 ; 1054-1500
ISSN (online)	1089-7682
ISSN	1054-1500
DOI	10.1063/5.0054459
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Article: The Role of Mixotrophy in Southern Ocean Ecosystems : The Sensitivity of Model Dynamics to the Magnitude and Form of Mixotroph Interactions Between Plankton

Norbury, John / Cropp, Roger / Moroz, Irene M

Environmental modeling and assessment. 2019 Aug., v. 24, no. 4

2019

Abstract: We investigate the influence of mixotrophy on the dynamical properties of a six-population model of a three–trophic level Southern Ocean ecosystem. We find that including mixotrophic interactions between the lowest trophic level populations can ... ...

Abstract	We investigate the influence of mixotrophy on the dynamical properties of a six-population model of a three–trophic level Southern Ocean ecosystem. We find that including mixotrophic interactions between the lowest trophic level populations can significantly influence the dynamics of the highest trophic level populations, and in extreme cases lead to extinctions. Significantly, not only is the strength of the mixotrophic interaction important, it matters how it is included in the model, as a specialist or generalist grazer. We note in particular that the generalist formulation is inappropriate for “green” mixotrophs that fuel the majority of their growth by photosynthesis. The model can have complicated dynamics when subject to large amplitude, regular forcing, suggesting the sea ice—salps link may be obfuscated by endogenous population oscillations. Further, we observe that constructing the model within the Conservative Normal framework allows insights into the bifurcation behaviour of the model.
Keywords	ecosystems ; models ; photosynthesis ; plankton ; trophic levels
Language	English
Dates of publication	2019-08
Size	p. 421-435.
Publishing place	Springer International Publishing
Document type	Article
ZDB-ID	2000915-X
ISSN	1573-2967 ; 1420-2026
ISSN (online)	1573-2967
ISSN	1420-2026
DOI	10.1007/s10666-019-09670-0
Database	NAL-Catalogue (AGRICOLA)

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Article: Mixotrophs: Dynamic disrupters of plankton systems?

Moroz, Irene M / Roger Cropp / John Norbury

Journal of sea research. 2019 May, v. 147

2019

Abstract: We consider a simple plankton model with one phytoplankton autotroph population, one mixotrophic phytoplankton population that both photosynthesises and consumes the other phytoplankton, and one zooplankton predator population. The zooplankton predator ... ...

Abstract	We consider a simple plankton model with one phytoplankton autotroph population, one mixotrophic phytoplankton population that both photosynthesises and consumes the other phytoplankton, and one zooplankton predator population. The zooplankton predator may be either a specialist or a generalist grazer on the phytoplankton. We examine the influence on the system's equilibrium points and dynamical properties of varying degrees of mixotrophy by the phytoplankton and grazing strategy by the zooplankton, both with and without the presence of seasonal forcing.We find that the strength of the mixotrophy interaction does not substantially change the equilibrium properties of the model across all grazing strategies, but it can have a substantial effect on the dynamical properties. Further, external forcings on typical phytoplankton or zooplankton time scales can in some circumstances substantially modify these dynamics. Our analyses suggest that plankton models developed to represent bio-geochemical processes in the ocean for applications in climate change modelling should be subjected to thorough equilibrium and dynamical analyses before being used for climate prediction.
Keywords	climate change ; climate models ; grazing ; phytoplankton ; zooplankton
Language	English
Dates of publication	2019-05
Size	p. 37-45.
Publishing place	Elsevier B.V.
Document type	Article
ISSN	1385-1101
DOI	10.1016/j.seares.2019.02.001
Database	NAL-Catalogue (AGRICOLA)

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Article: Chaos in plankton models: Foraging strategy and seasonal forcing

Moroz, Irene M / John Norbury / Roger Cropp

Ecological modelling. 2016 July 24, v. 332

2016

Abstract: The dynamics of plankton ecosystems have long been of interest to ecologists and mathematicians, with some of the earliest examples of chaotic dynamics being provided by ecological models. Mortality terms were initially identified as determinants of ... ...

Abstract	The dynamics of plankton ecosystems have long been of interest to ecologists and mathematicians, with some of the earliest examples of chaotic dynamics being provided by ecological models. Mortality terms were initially identified as determinants of chaos in simple ecosystem models, but relatively little attention has been given to the role of grazing terms. The behaviour of omnivores has arisen as a particularly interesting case. Recent experiments have revealed that plankton omnivores may change their feeding behaviour in response to changes in temperature, and is therefore of interest to plankton modellers contributing models of biogeochemical cycling in the ocean to climate models. In this paper we consider the role of an omnivorous zooplankton's foraging strategy, seasonal variations and the choice of functional forms on the dynamics of a simple two prey–one predator plankton model, within a Conservative-Normal framework. We find that assumptions about the way the predator forages for food, the specific form for grazing and mortality terms, and seasonal changes in the environment all qualitatively affect the predictions that the model will produce. In particular, discriminate foraging and seasonal variations engender chaotic dynamics while Holling Type III grazing and quadratic mortality terms suppress chaotic dynamics.
Keywords	biogeochemical cycles ; climate models ; ecosystems ; forage ; foraging ; functional response models ; grazing ; mortality ; omnivores ; prediction ; seasonal variation ; temperature ; zooplankton
Language	English
Dates of publication	2016-0724
Size	p. 103-111.
Publishing place	Elsevier B.V.
Document type	Article
ZDB-ID	191971-4
ISSN	0304-3800
ISSN	0304-3800
DOI	10.1016/j.ecolmodel.2016.04.011
Database	NAL-Catalogue (AGRICOLA)

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Article ; Online: Hidden hyperchaos and electronic circuit application in a 5D self-exciting homopolar disc dynamo.

Wei, Zhouchao / Moroz, Irene / Sprott, J C / Akgul, Akif / Zhang, Wei

Chaos (Woodbury, N.Y.)

2017 Volume 27, Issue 3, Page(s) 33101

Abstract: We report on the finding of hidden hyperchaos in a 5D extension to a known 3D self-exciting homopolar disc dynamo. The hidden hyperchaos is identified through three positive Lyapunov exponents under the condition that the proposed model has just two ... ...

Abstract	We report on the finding of hidden hyperchaos in a 5D extension to a known 3D self-exciting homopolar disc dynamo. The hidden hyperchaos is identified through three positive Lyapunov exponents under the condition that the proposed model has just two stable equilibrium states in certain regions of parameter space. The new 5D hyperchaotic self-exciting homopolar disc dynamo has multiple attractors including point attractors, limit cycles, quasi-periodic dynamics, hidden chaos or hyperchaos, as well as coexisting attractors. We use numerical integrations to create the phase plane trajectories, produce bifurcation diagram, and compute Lyapunov exponents to verify the hidden attractors. Because no unstable equilibria exist in two parameter regions, the system has a multistability and six kinds of complex dynamic behaviors. To the best of our knowledge, this feature has not been previously reported in any other high-dimensional system. Moreover, the 5D hyperchaotic system has been simulated using a specially designed electronic circuit and viewed on an oscilloscope, thereby confirming the results of the numerical integrations. Both Matlab and the oscilloscope outputs produce similar phase portraits. Such implementations in real time represent a new type of hidden attractor with important consequences for engineering applications.
Language	English
Publishing date	2017
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	1472677-4
ISSN	1089-7682 ; 1054-1500
ISSN (online)	1089-7682
ISSN	1054-1500
DOI	10.1063/1.4977417
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Article ; Online: Exploiting nonlinear recurrence and fractal scaling properties for voice disorder detection.

Little, Max A / McSharry, Patrick E / Roberts, Stephen J / Costello, Declan A E / Moroz, Irene M

Biomedical engineering online

2007 Volume 6, Page(s) 23

Abstract: Background: Voice disorders affect patients profoundly, and acoustic tools can potentially measure voice function objectively. Disordered sustained vowels exhibit wide-ranging phenomena, from nearly periodic to highly complex, aperiodic vibrations, and ... ...

Abstract	Background: Voice disorders affect patients profoundly, and acoustic tools can potentially measure voice function objectively. Disordered sustained vowels exhibit wide-ranging phenomena, from nearly periodic to highly complex, aperiodic vibrations, and increased "breathiness". Modelling and surrogate data studies have shown significant nonlinear and non-Gaussian random properties in these sounds. Nonetheless, existing tools are limited to analysing voices displaying near periodicity, and do not account for this inherent biophysical nonlinearity and non-Gaussian randomness, often using linear signal processing methods insensitive to these properties. They do not directly measure the two main biophysical symptoms of disorder: complex nonlinear aperiodicity, and turbulent, aeroacoustic, non-Gaussian randomness. Often these tools cannot be applied to more severe disordered voices, limiting their clinical usefulness. Methods: This paper introduces two new tools to speech analysis: recurrence and fractal scaling, which overcome the range limitations of existing tools by addressing directly these two symptoms of disorder, together reproducing a "hoarseness" diagram. A simple bootstrapped classifier then uses these two features to distinguish normal from disordered voices. Results: On a large database of subjects with a wide variety of voice disorders, these new techniques can distinguish normal from disordered cases, using quadratic discriminant analysis, to overall correct classification performance of 91.8 +/- 2.0%. The true positive classification performance is 95.4 +/- 3.2%, and the true negative performance is 91.5 +/- 2.3% (95% confidence). This is shown to outperform all combinations of the most popular classical tools. Conclusion: Given the very large number of arbitrary parameters and computational complexity of existing techniques, these new techniques are far simpler and yet achieve clinically useful classification performance using only a basic classification technique. They do so by exploiting the inherent nonlinearity and turbulent randomness in disordered voice signals. They are widely applicable to the whole range of disordered voice phenomena by design. These new measures could therefore be used for a variety of practical clinical purposes.
MeSH term(s)	Algorithms ; Artificial Intelligence ; Diagnosis, Computer-Assisted/methods ; Discriminant Analysis ; Fractals ; Humans ; Nonlinear Dynamics ; Pattern Recognition, Automated/methods ; Reproducibility of Results ; Sensitivity and Specificity ; Speech Disorders/diagnosis ; Speech Production Measurement/methods
Language	English
Publishing date	2007-06-26
Publishing country	England
Document type	Comparative Study ; Evaluation Studies ; Journal Article ; Research Support, Non-U.S. Gov't
ISSN	1475-925X
ISSN (online)	1475-925X
DOI	10.1186/1475-925X-6-23
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Exploiting Nonlinear Recurrence and Fractal Scaling Properties for Voice Disorder Detection

Roberts Stephen J / McSharry Patrick E / Little Max A / Costello Declan AE / Moroz Irene M

BioMedical Engineering OnLine, Vol 6, Iss 1, p

2007 Volume 23

Abstract: Abstract Background Voice disorders affect patients profoundly, and acoustic tools can potentially measure voice function objectively. Disordered sustained vowels exhibit wide-ranging phenomena, from nearly periodic to highly complex, aperiodic ... ...

Abstract	Abstract Background Voice disorders affect patients profoundly, and acoustic tools can potentially measure voice function objectively. Disordered sustained vowels exhibit wide-ranging phenomena, from nearly periodic to highly complex, aperiodic vibrations, and increased "breathiness". Modelling and surrogate data studies have shown significant nonlinear and non-Gaussian random properties in these sounds. Nonetheless, existing tools are limited to analysing voices displaying near periodicity, and do not account for this inherent biophysical nonlinearity and non-Gaussian randomness, often using linear signal processing methods insensitive to these properties. They do not directly measure the two main biophysical symptoms of disorder: complex nonlinear aperiodicity, and turbulent, aeroacoustic, non-Gaussian randomness. Often these tools cannot be applied to more severe disordered voices, limiting their clinical usefulness. Methods This paper introduces two new tools to speech analysis: recurrence and fractal scaling, which overcome the range limitations of existing tools by addressing directly these two symptoms of disorder, together reproducing a "hoarseness" diagram. A simple bootstrapped classifier then uses these two features to distinguish normal from disordered voices. Results On a large database of subjects with a wide variety of voice disorders, these new techniques can distinguish normal from disordered cases, using quadratic discriminant analysis, to overall correct classification performance of 91.8 ± 2.0%. The true positive classification performance is 95.4 ± 3.2%, and the true negative performance is 91.5 ± 2.3% (95% confidence). This is shown to outperform all combinations of the most popular classical tools. Conclusion Given the very large number of arbitrary parameters and computational complexity of existing techniques, these new techniques are far simpler and yet achieve clinically useful classification performance using only a basic classification technique. They do so by exploiting the inherent nonlinearity and turbulent randomness in disordered voice signals. They are widely applicable to the whole range of disordered voice phenomena by design. These new measures could therefore be used for a variety of practical clinical purposes.
Keywords	Medicine (General) ; R5-920 ; Medicine ; R ; DOAJ:Medicine (General) ; DOAJ:Health Sciences
Subject code	780
Language	English
Publishing date	2007-06-01T00:00:00Z
Publisher	BioMed Central
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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