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Book ; Online: Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors

Volos, Christos / Jafari, Sajad / Kengne, Jacques / Munoz-Pacheco, Jesus M. / Rajagopal, Karthikeyan

2019

Abstract: In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel ... ...

Abstract	In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors and hidden attractors. The localization of self-excited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with non-hyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phase-locked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with self-excited attractors and hidden attractors
Keywords	Technology (General) ; Engineering (General). Civil engineering (General)
Size	1 electronic resource (290 p.)
Publisher	MDPI - Multidisciplinary Digital Publishing Institute
Publishing place	Verlagsort nicht ermittelbar
Document type	Book ; Online
Note	eng ; Open Access
HBZ-ID	HT020195803
ISBN	9783038978985 ; 9783038978992 ; 3038978981 ; 303897899X
Database	ZB MED Catalogue: Medicine, Health, Nutrition, Environment, Agriculture

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Article ; Online: Complex dynamics in a fractional order nephron pressure and flow regulation model.

Rajagopal, Karthikeyan / Karthikeyan, Anitha

Bio Systems

2023 Volume 230, Page(s) 104931

Abstract: Cardiovascular diseases can be attributed to irregular blood pressure, which may be caused by malfunctioning kidneys that regulate blood pressure. Research has identified complex oscillations in the mechanisms used by the kidney to regulate blood ... ...

Abstract	Cardiovascular diseases can be attributed to irregular blood pressure, which may be caused by malfunctioning kidneys that regulate blood pressure. Research has identified complex oscillations in the mechanisms used by the kidney to regulate blood pressure. This study uses established physiological knowledge and earlier autoregulation models to derive a fractional order nephron autoregulation model. The dynamical behaviour of the model is analyzed using bifurcation plots, revealing periodic oscillations, chaotic regions, and multistability. A lattice array of the model is used to study collective behaviour and demonstrates the presence of chimeras in the network. A ring network of the fractional order model is also considered, and a diffusion coupling strength is adopted. A basin of synchronization is derived, considering coupling strength, fractional order or number of neighbours as parameters, and measuring the strength of incoherence. Overall, the study provides valuable insights into the complex dynamics of the nephron autoregulation model and its potential implications for cardiovascular diseases.
MeSH term(s)	Humans ; Cardiovascular Diseases ; Models, Biological ; Renal Circulation/physiology ; Nephrons/blood supply ; Nephrons/physiology ; Kidney
Language	English
Publishing date	2023-06-16
Publishing country	Ireland
Document type	Journal Article
ZDB-ID	186234-0
ISSN	1872-8324 ; 0303-2647
ISSN (online)	1872-8324
ISSN	0303-2647
DOI	10.1016/j.biosystems.2023.104931
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Article: Comparing the chondrogenic potential of rabbit mesenchymal stem cells derived from the infrapatellar fat pad, periosteum & bone marrow.

Rajagopal, Karthikeyan / Madhuri, Vrisha

The Indian journal of medical research

2022 Volume 154, Issue 5, Page(s) 732–742

Abstract: Background & objectives: Rabbit model is commonly used to demonstrate the proof of concept in cartilage tissue engineering. However, limited studies have attempted to find an ideal source of rabbit mesenchymal stem cells (MSCs) for cartilage repair. ... ...

Abstract	Background & objectives: Rabbit model is commonly used to demonstrate the proof of concept in cartilage tissue engineering. However, limited studies have attempted to find an ideal source of rabbit mesenchymal stem cells (MSCs) for cartilage repair. This study aimed to compare the in vitro chondrogenic potential of rabbit MSCs isolated from three sources namely infrapatellar fat pad (IFP), periosteum (P) and bone marrow (BM). Methods: Rabbit MSCs from three sources were isolated and characterized using flow cytometry and multi-lineage differentiation assay. Cell proliferation was assessed using trypan blue dye exclusion test; in vitro chondrogenic potential was evaluated by histology and gene expression and the outcomes were compared amongst the three MSC sources. Results: MSCs from three sources shared similar morphology and expressed >99 per cent positive for CD44 and CD81 and <3 per cent positive for negative markers CD34, CD90 and human leukocyte antigen - DR isotype (HLA-DR). The BM-MSCs and IFP-MSCs showed significantly higher cell proliferation (P<0.001) than the P-MSCs from passage 4. Histologically, BM-MSCs formed a thicker cartilage pellet (P<0.01) with abundant matrix deposition than IFP and P-MSCs during chondrogenic differentiation. The collagen type 2 staining was significantly (P<0.05) higher in BM-MSCs than the other two sources. These outcomes were further confirmed by gene expression, where the BM-MSCs demonstrated significantly higher expression (P<0.01) of cartilage-specific markers (COL2A1, SOX9 and ACAN) with less hypertrophy. Interpretation & conclusions: This study demonstrated that BM-MSCs had superior chondrogenic potential and generated better cartilage than IFP and P-MSCs in rabbits. Thus, BM-MSCs remain a promising candidate for rabbit articular cartilage regeneration.
MeSH term(s)	Adipose Tissue ; Animals ; Bone Marrow ; Bone Marrow Cells ; Cartilage, Articular ; Cell Differentiation/genetics ; Cells, Cultured ; Humans ; Mesenchymal Stem Cells ; Periosteum ; Rabbits
Language	English
Publishing date	2022-05-09
Publishing country	India
Document type	Journal Article
ZDB-ID	390883-5
ISSN	0971-5916 ; 0019-5340
ISSN	0971-5916 ; 0019-5340
DOI	10.4103/ijmr.IJMR_93_19
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Article ; Online: Synchronization Studies of Hindmarsh-Rose Neuron Networks: Unraveling the Influence of connection induced memristive synapse.

Joseph, Dianavinnarasi / Ramachandran, Raja / Karthikeyan, Anitha / Rajagopal, Karthikeyan

Bio Systems

2023 Volume 234, Page(s) 105069

Abstract: This study focuses on the synchronization analysis of Hindmarsh-Rose neurons coupled through a common memristor (coupled mHRN). Initially, we thoroughly examine the synchronization of two mHRNs coupled via a common memristor before exploring ... ...

Abstract	This study focuses on the synchronization analysis of Hindmarsh-Rose neurons coupled through a common memristor (coupled mHRN). Initially, we thoroughly examine the synchronization of two mHRNs coupled via a common memristor before exploring synchronization in a network of mHRNs. The stability of the proposed model is analyzed in three cases, demonstrating the existence of a single equilibrium point whose stability is influenced by external stimuli. The stable and unstable regions are investigated using eigenvalues. Through bifurcation analysis and the determination of maximum Lyapunov exponents, we identify chaotic and hyperchaotic trajectories. Additionally, using the next-generation matrix method, we calculate the chaotic number C
MeSH term(s)	Nonlinear Dynamics ; Synapses ; Neurons/physiology ; Cluster Analysis
Language	English
Publishing date	2023-11-07
Publishing country	Ireland
Document type	Journal Article
ZDB-ID	186234-0
ISSN	1872-8324 ; 0303-2647
ISSN (online)	1872-8324
ISSN	0303-2647
DOI	10.1016/j.biosystems.2023.105069
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Article ; Online: Dynamics, synchronization and traveling wave patterns of flux coupled network of Chay neurons.

Joseph, Dianavinnarasi / Kumar, Rakshanaa / Karthikeyan, Anitha / Rajagopal, Karthikeyan

Bio Systems

2023 Volume 235, Page(s) 105113

Abstract: Studies in the literature have demonstrated the significance of the synchronization of neuronal electrical activity for signal transmission and information encoding. In light of this importance, we investigate the synchronization of the Chay neuron model ...

Abstract	Studies in the literature have demonstrated the significance of the synchronization of neuronal electrical activity for signal transmission and information encoding. In light of this importance, we investigate the synchronization of the Chay neuron model using both theoretical analysis and numerical simulations. The Chay model is chosen for its comprehensive understanding of neuronal behavior and computational efficiency. Additionally, we explore the impact of electromagnetic induction, leading to the magnetic flux Chay neuron model. The single neuron model exhibits rich and complex dynamics for various parameter choices. We explore the bifurcation structure of the model through bifurcation diagrams and Lyapunov exponents. Subsequently, we extend our study to two coupled magnetic flux Chay neurons, identifying mode locking and structures reminiscent of Arnold's tongue. We evaluate the stability of the synchronized manifold using Lyapunov theory and confirm our findings through simulations. Expanding our study to networks of diffusively coupled flux Chay neurons, we observe coherent, incoherent, and imperfect chimera patterns. Our investigation of three network types highlights the impact of network topology on the emergent dynamics of the Chay neuron network. Regular networks exhibit diverse patterns, small-world networks demonstrate a critical transition to coherence, and random networks showcase synchronization at specific coupling strengths. These findings significantly contribute to our understanding of the synchronization patterns exhibited by the magnetic flux Chay neuron. To assess the synchronization stability of the Chay neuron network, we employ master stability function analysis.
MeSH term(s)	Models, Neurological ; Neurons/physiology ; Action Potentials/physiology
Language	English
Publishing date	2023-12-29
Publishing country	Ireland
Document type	Journal Article
ZDB-ID	186234-0
ISSN	1872-8324 ; 0303-2647
ISSN (online)	1872-8324
ISSN	0303-2647
DOI	10.1016/j.biosystems.2023.105113
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Article ; Online: Emergence of extreme events in a quasiperiodic oscillator.

Durairaj, Premraj / Kanagaraj, Sathiyadevi / Kumarasamy, Suresh / Rajagopal, Karthikeyan

Physical review. E

2023 Volume 107, Issue 2, Page(s) L022201

Abstract: Extreme events are unusual and rare large-amplitude fluctuations can occur unexpectedly in nonlinear dynamical systems. Events above the extreme event threshold of the probability distribution of a nonlinear process characterize extreme events. Different ...

Abstract	Extreme events are unusual and rare large-amplitude fluctuations can occur unexpectedly in nonlinear dynamical systems. Events above the extreme event threshold of the probability distribution of a nonlinear process characterize extreme events. Different mechanisms for the generation of extreme events and their prediction measures have been reported in the literature. Based on the properties of extreme events, such as those that are rare in the frequency of occurrence and extreme in amplitude, various studies have shown that extreme events are both linear and nonlinear in nature. Interestingly, in this Letter, we report on a special class of extreme events which are nonchaotic and nonperiodic. These nonchaotic extreme events appear in between the quasiperiodic and chaotic dynamics of the system. We report the existence of such extreme events with various statistical measures and characterization techniques.
Language	English
Publishing date	2023-03-17
Publishing country	United States
Document type	Journal Article
ZDB-ID	2844562-4
ISSN	2470-0053 ; 2470-0045
ISSN (online)	2470-0053
ISSN	2470-0045
DOI	10.1103/PhysRevE.107.L022201
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Article ; Online: Synchronization enhancement subjected to adaptive blinking coupling.

Irankhah, Reza / Mehrabbeik, Mahtab / Parastesh, Fatemeh / Rajagopal, Karthikeyan / Jafari, Sajad / Kurths, Jürgen

Chaos (Woodbury, N.Y.)

2024 Volume 34, Issue 2

Abstract: Synchronization holds a significant role, notably within chaotic systems, in various contexts where the coordinated behavior of systems plays a pivotal and indispensable role. Hence, many studies have been dedicated to investigating the underlying ... ...

Abstract	Synchronization holds a significant role, notably within chaotic systems, in various contexts where the coordinated behavior of systems plays a pivotal and indispensable role. Hence, many studies have been dedicated to investigating the underlying mechanism of synchronization of chaotic systems. Networks with time-varying coupling, particularly those with blinking coupling, have been proven essential. The reason is that such coupling schemes introduce dynamic variations that enhance adaptability and robustness, making them applicable in various real-world scenarios. This paper introduces a novel adaptive blinking coupling, wherein the coupling adapts dynamically based on the most influential variable exhibiting the most significant average disparity. To ensure an equitable selection of the most effective coupling at each time instance, the average difference of each variable is normalized to the synchronous solution's range. Due to this adaptive coupling selection, synchronization enhancement is expected to be observed. This hypothesis is assessed within networks of identical systems, encompassing Lorenz, Rössler, Chen, Hindmarsh-Rose, forced Duffing, and forced van der Pol systems. The results demonstrated a substantial improvement in synchronization when employing adaptive blinking coupling, particularly when applying the normalization process.
Language	English
Publishing date	2024-02-20
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	10.1063/5.0188366
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Article ; Online: Collective dynamics of a coupled Hindmarsh-Rose neurons with locally active memristor.

Kanagaraj, Sathiyadevi / Durairaj, Premraj / Sampath, Sivaperumal / Karthikeyan, Anitha / Rajagopal, Karthikeyan

Bio Systems

2023 Volume 232, Page(s) 105010

Abstract: A Locally active memristors can mimic neural synapses, resulting in rich neuro-morphological dynamics in biological neurons. To illustrate the impact of a local active memristive synapse, we consider coupled Hindmarsh-Rose (HR) neurons. Firstly, the ... ...

Abstract	A Locally active memristors can mimic neural synapses, resulting in rich neuro-morphological dynamics in biological neurons. To illustrate the impact of a local active memristive synapse, we consider coupled Hindmarsh-Rose (HR) neurons. Firstly, the dynamical transitions of the proposed system are investigated using bifurcation analysis and Lyapunov exponents, and we find that the transition between periodic and chaotic states depends on the input currents and memristive coupling strength. By performing the two-parameter analysis, the existence of periodic and chaotic regions is revealed. The collective behavior is then examined by expanding the network to include memristive coupled HR neurons under different network connectivities. We show that the system achieves synchronization behavior for all network connectivities, including regular, random, and small-world, when the strength of the memristive coupling is increased.
MeSH term(s)	Neurons ; Cluster Analysis ; Mass Behavior ; Synapses
Language	English
Publishing date	2023-08-24
Publishing country	Ireland
Document type	Journal Article
ZDB-ID	186234-0
ISSN	1872-8324 ; 0303-2647
ISSN (online)	1872-8324
ISSN	0303-2647
DOI	10.1016/j.biosystems.2023.105010
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Article ; Online: Theoretical study and circuit implementation of three chain-coupled self-driven Duffing oscillators.

Sundarambal, Balaraman / Kemgang, Lucas Kana / Jacques, Kengne / Rajagopal, Karthikeyan

Chaos (Woodbury, N.Y.)

2023 Volume 33, Issue 11

Abstract: In this paper, we describe the scenario from the birth of oscillations to multi-spiral chaos in a novel system composed of three chain-coupled self-driven Duffing oscillators. Eight of the equilibrium points develop (multiple) Hopf bifurcation when ... ...

Abstract	In this paper, we describe the scenario from the birth of oscillations to multi-spiral chaos in a novel system composed of three chain-coupled self-driven Duffing oscillators. Eight of the equilibrium points develop (multiple) Hopf bifurcation when varying a parameter (e.g., coupling coefficient). Considering the computer integration of the state equations, the combined exploitation of Lyapunov exponent plots, bifurcation diagrams, basins of attraction, and phase portraits, unusual and attractive features were highlighted including the coexistence of eight bifurcation branches, Hopf bifurcations, a multitude of coexisting types of oscillations and a six-spiral chaotic attractor, just to cite a few. Using basic electronic components, the electronic circuit of the three chain-coupled Duffing oscillator system is performed. Orcad-PSpice simulated dynamics of the proposed chain-coupled analog circuit confirm the theoretically disclosed features. Moreover, the practical feasibility of the coupled system is demonstrated by considering microcontroller-based hardware realization.
Language	English
Publishing date	2023-11-18
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	10.1063/5.0155047
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Article ; Online: Impact of external excitations on blinking enhanced synchronization in bistable vibrational energy harvesters.

Durairaj, Premraj / Kanagaraj, Sathiyadevi / Duraisamy, Prakash / Karthikeyan, Anitha / Rajagopal, Karthikeyan

Chaos (Woodbury, N.Y.)

2023 Volume 33, Issue 6

Abstract: Vibrational energy harvesters are capable of converting low-frequency broad-band mechanical energy into electrical power and can be used in implantable medical devices and wireless sensors. With the use of such energy harvesters, it is feasible to ... ...

Abstract	Vibrational energy harvesters are capable of converting low-frequency broad-band mechanical energy into electrical power and can be used in implantable medical devices and wireless sensors. With the use of such energy harvesters, it is feasible to generate continuous power that is more reliable and cost-effective. According to previous findings, the energy harvester can offer rich complex dynamics, one of which is obtaining the synchronization behavior, which is intriguing to achieve desirable power from energy harvesters. Therefore, we consider bistable energy harvesters with periodic and quasiperiodic excitations to investigate synchronization. Specifically, we introduce blinking into the coupling function to check whether it improves the synchronization. Interestingly, we discover that raising the normalized proportion of blinking can initiate synchronization behaviors even with lower optimal coupling strength than the absence of blinking in the coupling (i.e., continuous coupling). The existence of synchronization behaviors is confirmed by finding the largest Lyapunov exponents. In addition, the results show that the optimal coupling strength needed to achieve synchronization for quasiperiodic excitations is smaller than that for periodic excitations.
Language	English
Publishing date	2023-06-06
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	10.1063/5.0137668
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