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Master stability function (MSF) plays a substantial role in understanding the synchronisation behaviour of coupled nonlinear oscillators. Recent attention in the fractional calculus and its applications in nonlinear dynamics has expanded to investigate the network dynamics of them. Hence, we derive the MSF for couped fractional order nonlinear oscillators and investigate their relation with coupling strength and fractional order. To make the comparison between integer and fractional order MSF, we have used well known nonlinear oscillators for investigation. Similar to the integer order, the fractional order coupled nonlinear oscillators too exhibit MSFs which are analysed for existence of negative with in the finite interval of normalized coupling parameter value. We have used the same classifications of integer order MSFs to define different classes for fractional order MSF’s. By using numerical simulations, we could show that majority of fractional order coupled oscillators exhibit higher classes of MSF confirming better synchronisation compared to their integer order counterparts.

A chaotic simple jerk system (SJS) that belongs to systems with self-excited and hidden attractors is introduced in this paper. The dynamics of the proposed SJS is analytically and numerically investigated. Interestingly, the influence of the time delay on the proposed chaotic SJS is studied. In addition, the physical existence of self-excited and hidden chaotic attractors found in the proposed SJS and in the time-delayed form of SJSs (TDSJSs) are verified by using Orcard-PSpice software. Finally, chaos synchronization of identical, unidirectional, coupled, proposed chaotic TDSJSs is also reported.

An autonomous five-dimensional (5D) system with offset boosting is constructed by modifying the well-known three-dimensional autonomous Liu and Chen system. Equilibrium points of the proposed autonomous 5D system are found and its stability is analyzed. The proposed system includes Hopf bifurcation, periodic attractors, quasi-periodic attractors, a one-scroll chaotic attractor, a double-scroll chaotic attractor, coexisting attractors, the bistability phenomenon, offset boosting with partial amplitude control, reverse period-doubling, and an intermittency route to chaos. Using a field programmable gate array (FPGA), the proposed autonomous 5D system is implemented and the phase portraits are presented to check the numerical simulation results. The chaotic attractors and coexistence of the attractors generated by the FPGA implementation of the proposed system have good qualitative agreement with those found during the numerical simulation. Finally, a sound data encryption and communication system based on the proposed autonomous 5D chaotic system is designed and illustrated through a numerical example.

This paper investigates the dynamical behavior of a single and a network of current modulated edge emitting semiconductor lasers (CMEESLs). Different dynamical behaviors of CMEESL are revealed in two-dimensional parameters space by varying the amplitude and frequency of modulation. Single CMEESL exhibits periodic pulse packages followed by period-doubling cascade to chaotic pulse packages for frequency of modulation current density less than 1 GHz. Microcontroller results which agree with numerical results of single CMEESL are presented. To investigate the dynamics in a network of CMEESLs, a nonlocally coupled lattice array of CMEESLs is analyzed numerically by varying the coupling strength. It is found that the coupling strength plays a significant role in the coherent and incoherent behaviors of the nodes in the network. For a small range of coupling strength, the network exhibits chimera states which are confirmed by their respective state plots. Synchronization error between the nonlocally coupled CMEESLs is also presented to show the existence of chimera states.

The discrete system serves an important role in mimicking collective dynamics found in continuous dynamical systems, which are relevant to many realistic natural and artificial systems. To investigate the dynamical transition of a discrete system, we employ three-dimensional sinusoidal discrete maps with an additional self feedback factor. Specifically, we focus on dynamical transitions with respect to the bifurcation parameter, sine function amplitude, and intensity of self feedback factors. We demonstrate the presence of symmetry in relation to parametric variation using two parameter diagrams. The study is then expanded to the network of sine maps in the presence of self-feedback factor. We discover that negative feedback exhibits the transition from cluster state to synchronization while raising the coupling strength for small-world network interactions. Furthermore, increasing feedback from negative to positive causes the transition from synchronization to desynchronization via chimera state for various complex network connectivities.

The fractional order model of a glucose-insulin regulatory system is derived and presented. It has been extensively proved in the literature that fractional order analysis of complex systems can reveal interesting and unexplored features of the system. In our investigations we have revealed that the glucose-insulin regulatory system shows multistability and antimonotonicity in its fractional order form. To show the effectiveness of fractional order analysis, all numerical investigations like stability of the equilibrium points, Lyapunov exponents, and bifurcation plots are derived. Various biological disorders caused by an unregulated glucose-insulin system are studied in detail. This may help better understand the regulatory system.

In this paper, a multiscroll snap oscillator with hyperbolic tangent function is proposed. There is no limitation in the number of scrolls and it can be increased by proper choice of a specific function. The Lyapunov exponents of the proposed system are obtained to testify the chaotic behavior of the system. Fractional order multiscroll system is derived from its integer order model by using the Adams–Bashforth–Moulton algorithm. A new scheme is applied in order to investigate the synchronization of the multiscroll systems. The main objective of the paper is to propose a multiscroll attractor and show that the number of scrolls can be controlled by the only nonlinear function. Such systems are less investigated in the literatures and has many real time applications like image and voice encryption, random number generators, chaos based communication systems and so on.

In this paper a modified third order Wien bridge oscillator with fractional order memristor is proposed. Various dynamical properties of the proposed oscillator are investigated such as equilibrium points, Eigenvalues, Lyapunov exponents and bifurcation diagrams. The Lyapunov spectrum of the system for various values of fractional order is derived. Using forward and backward continuation methods of plotting bifurcation diagram, the multistability of the oscillator is investigated. The proposed oscillator is realized using Field Programmable Gate Arrays and the experiment is conducted using hardware-software co-simulation.

We propose a modified Fitzhugh-Nagumo neuron (MFNN) model. Based on this model, an integer-order MFNN system (case A) and a fractional-order MFNN system (case B) were investigated. In the presence of electromagnetic induction and radiation, memductance and induction can show a variety of distributions. Fractional-order magnetic flux can then be considered. Indeed, a fractional-order setting can be acceptable for non-uniform diffusion. In the case of an MFNN system with integer-order discontinuous magnetic flux, the system has chaotic and non-chaotic attractors. Dynamical analysis of the system shows the birth and death of period doubling, which is a sign of antimonotonicity. Such a behavior has not been studied previously in the dynamics of neurons. In an MFNN system with fractional-order discontinuous magnetic flux, different attractors such as chaotic and periodic attractors can be observed. However, there is no sign of antimonotonicity.

Understanding neuron function may aid in determining the complex collective behavior of brain systems. To delineate the collective behavior of the neural network, we consider modified tabu learning neurons (MTLN) with magnetic flux. Primarily, we explore the rest points and stability of the isolated MTLN, as well as its dynamical characteristics using maximal Lyapunov exponents. Surprisingly, we discover that for a given set of parameter values with distinct initial conditions, the periodic and the chaotic attractors may coexist. In addition, experimental analysis is carried out using a microcontroller-based implementation technique to support the observed complex behavior of the MTLN. We demonstrate that the observed numerical results are in good agreement with the experimental verification. Eventually, the collective behaviors of the considered MTLN are investigated by extending them to the network of the lattice array. We discover that when the magnetic flux coupling coefficient is varied in the presence of an external stimulus, the transition from spiral waves to traveling plane waves occurs. Finally, we manifest the formation of spiral waves in the absence of an external stimulus in contrast to previous observations.

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.

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.

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 harvester. Various dynamical properties are explored, and the bifurcation plots of the periodically excited harvester shows 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 can be efficient if the chaotic regimes can be suppressed and hence we focus our discussion towards 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.

Memristor-based oscillators are of recent interest, and hence, in this paper, we introduce a new Wien bridge oscillator with a fractional-order memristor. The novelty of the proposed oscillator is the multistability feature and the wide range of fractional orders for which the system shows chaos. We have investigated the various dynamical properties of the proposed oscillator and have presented them in detail. The oscillator is then realized using off-the-shelf components, and the results are compared with that of the numerical results. A combination synchronization scheme is proposed which uses more than one driver systems to synchronize with one response system. Indeed, we use two different techniques where the first one consists of splitting the transmitted signals into two parts where each part is loaded in different drive systems, while the second one consists of dividing time into different intervals and loading the signals in different drive systems. Such techniques improve the antiattack capability of the systems when used for secure communication.

In this paper, a new jerk system is designed. This system can display different characters of equilibrium points according to the value of its parameters. The proposed nonlinear oscillator can have both self-excited and hidden attractors. Dynamical properties of this system are investigated with the help of eigenvalues of equilibria, Lyapunov exponents' spectrum, and bifurcation diagrams. Also, an electronic circuit implementation is carried out to show the feasibility of this system. As an engineering application of this new chaotic jerk system, a chaotic communication system is realized by correlation delay shift keying. When the results of the communication system are examined, the transmitted information signal is successfully obtained in the receiving unit, and its performance efficiency is investigated in the presence of additive white Gaussian noise.

PURPOSE: Scrub typhus an acute febrile illness has diverse clinical manifestations, which overlap with other febrile illnesses. Due to this reason, it is misdiagnosed, leading to inappropriate treatment, sometimes resulting in fatality. Thus, accurate diagnosis of scrub typhus is important for appropriate treatment. This study evaluated the loop-mediated isothermal amplification (LAMP) assay as a diagnostic test for scrub typhus among patients with fever. MATERIALS AND METHODS: A total of 50 cases of acute febrile illness clinically resembling scrub typhus, with or without an eschar, or cases of pyrexia of unknown origin were included in the study. Blood samples collected from these cases were subjected to detection of IgM antibodies to Orientia tsutsugamushi by ELISA, conventional groEL polymerase chain reaction (PCR), and the LAMP assay. RESULTS: Twelve cases had fever for less than a week, and two had fever for more than 3 weeks. IgM antibodies to O. tsutsugamushi were detected in 37 out of 50 samples (74%). LAMP assay was positive in 33 samples (66%). groEL gene-based PCR detected 35 (70%) samples as positive. Two samples negative by LAMP assay were positive by this PCR. Twenty samples collected from patients with dengue, typhoid, and malaria tested by the LAMP assay were negative, indicating its good specificity. LAMP assay and the conventional groEL-based PCR could detect 72.7% and 74.3% of the samples, respectively before the 10th day after onset of fever, whereas IgM ELISA could detect only 40.5% of the 37 samples. CONCLUSION: This study suggests that LAMP assay could be a useful diagnostic test for detecting scrub typhus in the acute phase of the illness and a cheaper alternative to other molecular methods in resource poor settings.

An extended Morris–Lecar neuron model incorporating electromagnetic flux coupling and external excitation is proposed. The complete dynamical behavior of the new model is investigated as autonomous and non-autonomous forms. Multistability and coexisting attractors are shown for the new neuron model. It is shown that when external excitation is introduced, the complete dynamical behavior of the system changes compared to the non-excited version. To study the wave propagation pattern, we construct a network of the extended neuron model and study the generation of spiral waves under various conditions of coupling strength, stimuli parameters and system parameters. We have also studied the wave propagation pattern considering the time-based chaotic-periodic neurons in the network.

The last two decades have seen many literatures on the mathematical and computational analysis of neuronal activities resulting in many mathematical models to describe neuron. Many of those models have described the membrane potential of a neuron in terms of the leakage current and the synaptic inputs. Only recently researchers have proposed a new neuron model based on the electromagnetic induction theorem, which considers inner magnetic fluctuation and external electromagnetic radiation as a significant missing part that can participate in neural activity. While the flux coupling of the membrane is considered equivalent to a memductance function of a memristor, standard memductance model of $$\alpha + 3\beta \phi^{2}$$ has been used in the literatures, but in this paper we propose a new memductance function based on discontinuous flux coupling. Various dynamical properties of the neuron model with discontinuous flux coupling are studied and interestingly the proposed model shows hyperchaotic behavior which was not identified in the literatures. Furthermore, we consider a ring network of the proposed model and investigate whether the chimera state can emerge. The chimera state relates to the state with simultaneously coherence and incoherence in oscillatory networks and has received much attention in recent years.

Discovering chaotic systems with interesting features has been of interest in the recent years. One such important and interesting feature is the type and shape of equilibrium points. We introduce a class of chaotic systems which could show different types of infinite equilibrium points. The fundamental properties of the proposed systems like bifurcation diagram and Lyapunov exponents are investigated. An electronic circuit of the presented chaotic systems is implemented. In addition, a chaos-based communication application by the differential chaos shift keying method with the new chaotic system is designed and tested for engineering application. According to the design test results, the proposed chaos-based communication system is successful. Therefore, the new chaotic system can be used in chaos-based communication systems.

In this paper, we report a novel chaotic snap oscillator with one nonlinear function. Dynamic analysis of the system shows the existence of bistability. To study the time delay effects on the proposed snap oscillator, we introduce multiple time delay in the fourth state equation. Investigation of dynamical properties of the time-delayed system shows that the snap oscillator exhibits the same multistable properties as the nondelayed system. The new multistable hyperjerk chaotic system has been tested in chaos shift keying and symmetric choc shift keying modulated communication designs for engineering applications. It has been determined that the symmetric chaos shift keying modulated communication system implemented with the new chaotic system is more successful than the chaos shift keying modulation for secure communication. Also, circuit implementation of the chaotic snap oscillator with tangent function is carried out showing its feasibility.

A newly introduced charge-controlled memcapacitor-based hyperchaotic oscillator with coexisting chaotic attractors is investigated. Dynamic analysis of the oscillator shows that it has infinite number of equilibrium points and shows multistability. Its multistability analysis in the parameter space shows the existence of chaotic and hyperchaotic attractors. Fractional-order analysis of the hyperchaotic oscillator shows that the hyperchaos remains in the fractional order too. Field programmable gate arrays are used to realize the proposed oscillator.

The dynamical behavior of the neurons directly depends on the transition from resting to spiking states. These transitions show different types of bifurcations and has different spiking periods. The transitions are also affected by the temperature exposure of the ionic channels. To understand such effects, we investigate the Morris-Lecar (ML) neuron model with temperature affected calcium, potassium and leak current channels. The presented ML model is considered with electromagnetic field coupling considering a simple cubic memristor flux relation. Firstly the basic dynamical properties of the ML model is analyzed considering the current temperature as the control parameter. The temperature affected ionic channels in the ML model leads to various types of oscillations from periodic spiking to chaotic bursting. These bifurcation patterns are well discussed with corresponding Lyapunov exponents. To study the wave propagation in the temperature dependent ML model (TDML), we have constructed two different types of network structure. In the first a simple lattice network is considered with the local nodes of the TDML neurons and the temperature effects on the wave propagation is studied individually for the three channels. In the second type of network, we have considered inter coupled three lattice layers of TDML neurons. This discussion is subdivided in to two cases and in the first case the layers are constructed such that the first, second and third layers having temperature affected calcium, potassium and leaky current channels respectively. In the second case we considered only one channel to have temperature effects and the others have no temperature affected ion channels. The wave propagation phenomenon in both the types of network is analyzed considering the current temperature as the control parameter.

In this paper we investigate the control of three-dimensional non-autonomous fractional-order uncertain model of a permanent magnet synchronous generator (PMSG) via a adaptive control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the literatures. Various dynamic properties of the fractional order model like eigen values, Lyapunov exponents, bifurcation and bicoherence are investigated. The system chaotic behavior for various orders of fractional calculus are presented. An adaptive controller is derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the robust controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results derived through which we show that for the derived adaptive controller and the parameter update law, the origin of the system for any bounded initial conditions is asymptotically stable.

In this paper, the effect of quasi-periodic excitation on a three-leg supporter configured with shape memory alloy is investigated. We derived the equation of motion for the system using the supporter configuration and polynomial constitutive model of the shape memory alloys (SMAs) based on Falk model. Two sets of parameters and symmetric initial conditions are used to analyze the system. The system responded with a chaotic attractor and a strange nonchaotic attractor. Coexistence of these attractors is studied and discussed with corresponding phase portrait, bifurcation plot, and cross section of basin of attraction. We confirm the quasi-periodic excitation results with generation of strange nonchaotic attractors as discussed in the literature. The special properties like symmetricity and bistability are revealed and the parameter ranges of existence of such behaviors are discussed. The system is analyzed for different phases and the existence of bistability in martensite phase and transition phase is explained. While the system enters into austenite phase, the bistability behavior vanishes. The results provide insight knowledge into dynamical response of a quasi-periodically excited SMA leg support system and will be useful for design improvements and controller design.