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We investigated the correlation among brain and leg muscle activations by analyzing Electroencephalogram (EEG) and Electromyogram (EMG) signals in different conditions. Twelve subjects performed four tasks, including (1) quarter turns, (2) U-turns, (3) bypass obstacles, and (4) repeating quarter turns and U-turns two times. Then, we quantified the alterations of the complexity of these signals by computing the fractal dimension and sample entropy. The results showed that EEG and EMG signals in the case of the first task are more complex than the second task, in which they are more complex than the third task. Furthermore, the brain and muscle signals show the least complexity in the case of the fourth task. Moreover, we found strong correlations in the variations of fractal dimension ([Formula: see text]) and sample entropy ([Formula: see text]) between EEG and EMG signals in various tasks. Therefore, brain and muscle activations are strongly correlated in different tasks. Similar analyses can be conducted in the case of other organs to decode their correlations.

Decoding of the coupling among the brain and heart activations is an important research area in network physiology. We studied the coupling of brain and heart activations for 48 subjects who performed the NASA Revised Multi-Attribute Task Battery II under three different activity level conditions. During the experiment, the physical activity of subjects was manipulated by changing the speed of a stationary bike (including no movement, 50[Formula: see text]rpm, and 70[Formula: see text]rpm) or a treadmill (including no movement, 3[Formula: see text]km/h, and 5[Formula: see text]km/h), while their physiological signals were recorded. We analyzed the complex structure of electroencephalogram (EEG) and R-R signals using fractal theory and sample entropy. The results demonstrated that the alterations of the complex structures of EEG and R-R signals are strongly correlated, which indicates the coupling between brain and heart activations. This method of analysis can be applied to evaluate the coupling between different organs.

This paper explore the dynamics, Field Programmable Gate Array (FPGA) validation of an autonomous piecewise damping Josephson junction jerk oscillator (APDJJJO) and uses it to protect medical images based on random number generator (RNG). APDJJJO is derived from a piecewise damping Josephson junction (JJ) model and has either no equilibrium points or two unstable equilibrium points. One-scroll chaotic hidden attractor, one-scroll sovereign complex attractor, periodic and one-scroll complex self-driven attractors coexisting, and bistable limit cycles are found in APDJJJO during the investigation based on numerical simulations. Additionally, the FPGA validation of the APDJJJO shows similar complex characteristics to those obtained during the investigation via numerical simulations. Lastly, the chaotic characteristics depicted by the APDJJJO are used to design a RNG for the encryption of medical images. The generated random bits are validated successfully by standard statistical tool set by the National Institute of Standards and Technology (NIST-800-22). Encryption algorithm is developed to secure a medical image by exploring the unpredicted bits generated. The safety and performances analysis are done to prove the robustness and efficiency of the image encryption algorithm.

This paper reports the field programmable gate array (FPGA) implementation of an autonomous Josephson junction jerk oscillator (AJJJO) and the investigated coexisting and chaotic attractors besteered, with different synchronization achieved. AJJJO displays bistability, megastability, and coexistence between limit cycle and self-excited chaotic attractors, which is validated by the FPGA implementation. The elimination of chaotic dynamics exhibited by AJJJO was done by using a double single controller via numerical simulations. The coexisting attractors between limit cycle and self-excited chaotic attractors are destroyed and besteered to the wanted path via the linear augmentation control method. Moreover, controllers are employed to achieve the difference synchronization of three identical coupled chaotic AJJJOs resulting from various starting conditions. Finally, numerical simulations of three identical coupled chaotic AJJJOs indicate the effectiveness of the difference synchronization.

In this paper, we analyzed the variations in brain activation between different activities. Since Electroencephalogram (EEG) signals as an indicator of brain activation contain information and have complex structures, we employed complexity and information-based analysis. Specifically, we used fractal theory and Shannon entropy for our analysis. Eight subjects performed three different activities (standing, walking, and walking with a brain–computer interface) while their EEG signals were recorded. Based on the results, the complexity and information content of EEG signals have the greatest and smallest values in walking and standing, respectively. Complexity and information-based analysis can be applied to analyze the activations of other organs in different conditions.

Map-based neuronal models have received much attention due to their high speed, efficiency, flexibility, and simplicity. Therefore, they are suitable for investigating different dynamical behaviors in neuronal networks, which is one of the recent hottest topics. Recently, the memristive version of the Rulkov model, known as the m-Rulkov model, has been introduced. This paper investigates the network of the memristive version of the Rulkov neuron map to study the effect of the memristor on collective behaviors. Firstly, two m-Rulkov neuronal models are coupled in different cases, through electrical synapses, chemical synapses, and both electrical and chemical synapses. The results show that two electrically coupled memristive neurons can become synchronous, while the previous studies have shown that two non-memristive Rulkov neurons do not synchronize when they are coupled electrically. In contrast, chemical coupling does not lead to synchronization; instead, two neurons reach the same resting state. However, the presence of both types of couplings results in synchronization. The same investigations are carried out for a network of 100 m-Rulkov models locating in a ring topology. Different firing patterns, such as synchronization, lagged-phase synchronization, amplitude death, non-stationary chimera state, and traveling chimera state, are observed for various electrical and chemical coupling strengths. Furthermore, the synchronization of neurons in the electrical coupling relies on the network's size and disappears with increasing the nodes number.

This work proposes a new chaotic jerk system with septic nonlinearity. The new system presents odd symmetry and undergoes typical behaviors including period doubling, merging crisis, spontaneous symmetry breaking, coexisting attractors and coexisting bubbles of bifurcations as well. The most gratifying feature discovered in this article, is the occurrence of up to eight coexisting attractors for appropriate sets of parameters. This latter feature is uncommon for a chaotic system as simple as the model proposed in this work (e.g. not reported in cubic, quintic or hyperbolic sine models). Multistability control is achieved by following the linear augmentation approach. We numerically prove that the multistable septic chaotic system can be adjusted to develop a monostable behavior when smoothly monitoring the coupling strength. More interestingly, it is found that the coupling breaks the symmetry of the chaotic jerk system and thus induces new patterns including asymmetric Hopf bifurcations; coexisting non-symmetric bubbles, critical phenomena, coexisting multiple asymmetric attractors, just to name a few. On this line, the linear augmentation scheme can be regarded as a simple means for inducing new features in odd symmetric chaotic systems. PSPICE simulation results captured from an electronic analog of the proposed septic jerk system are consistent with the theoretical investigations.

This paper introduces a simple 1-dimensional map-based model of spiking neurons. During the past decades, dynamical models of neurons have been used to investigate the biology of human nervous systems. The models simulate experimental records of neurons' voltages using difference or differential equations. Difference neuronal models have some advantages besides the differential ones. They are usually simpler, and considering the cost of needed computations, they are more efficient. In this paper, a simple 1-dimensional map-based model of spiking neurons is introduced. Sample entropy is applied to analyze the complexity of the model's dynamics. The model can generate a wide range of time series with different firing rates and different levels of complexities. Besides, using some tools like bifurcation diagrams and cobwebs, the introduced model is analyzed.

The master stability function (MSF) is a tool to evaluate the local stability of the synchronization in coupled oscillators. Computing the MSF of a network of a specific oscillator results in a curve whose shape is dependent on the nodes' dynamics, network topology, coupling function, and coupling strength. This paper calculates the MSF of networks of two diffusively coupled oscillators by considering different single variable and multi-variable couplings. Then, the linearity of the MSF is investigated by fitting a straight line to the MSF curve, and the root mean square error is obtained. It is observed that the multi-variable coupling with equal coefficients on all variables results in a linear MSF regardless of the dynamics of the nodes.

We investigate the impact of a broken symmetry on the dynamics of the well-known Shinriki oscillator. The broken symmetry is caused by the memristive diodes bridge with an asymmetric pinched hysteresis loop current–voltage characteristic designed by selecting two pairs of semiconductor diodes with different electrical properties. We examine how the broken symmetry affects the topology of attractors, the nature of fixed points, the bifurcation structures, the number and types of coexisting solutions, and the topology of the basins of attraction as well. These features are highlighted by utilizing plots of Lyapunov exponents, bifurcation diagrams, basins of attraction and phase portraits. As sample results, up to four coexisting asymmetric chaotic and periodic attractors are reported following changes in both initial conditions and parameters. Moreover, some sets of parameters are revealed where the system develops the striking feature of coexisting bubbles of bifurcation. Breadboard experiments are carried out to support the theoretical investigations. Although the breaking of symmetry may be seen as a common practice to discover new nonlinear events, the results obtained in this work may help for a better understanding of the impact of a real memristor on the global behavior of chaotic oscillators including a memristor as nonlinear device.

The study of complex nonlinear phenomena certainly represents a very hot ongoing research topic owing to recently published works. While a large number of contributions deal with systems with symmetry, very few works are concerned with those without any symmetry property. In this contribution, we introduce a novel asymmetric jerk system whose nonlinearity is in the form of a six-order Tchebytchev polynomial of the fundamental variable. The new system distinguishes by the presence of six equilibrium points symmetrically distributed along the x-axis. Three of these points are always unstable (regardless the values of parameter) while each of the three others undergoes Hopf type bifurcation at three different critical values of the control parameter resulting to self-excited coexisting behaviors such as: (i) a limit cycle and a pair of stable fixed points; (ii) a pair of limit cycles and a stable fixed point; (iii) a stable fixed point, a limit cycle and a chaotic attractor; just to cite a few. These features are studied by combining both analytical and numerical methods. More importantly, various parameter ranges are depicted where the new jerk system with Tchebytchev polynomials demonstrates extremely complex and striking nonlinear patterns such as antimonotonicity, hysteresis and coexisting bifurcation branches. These two latter properties give rise to multiple (i.e. two, three or four) coexisting (periodic and chaotic) attractors. Cross sections of the basins of attraction are provided to illustrate the magnetization of the state space caused by the various competing dynamics. The control of multistability in the new system is achieved via linear augmentation scheme. The practical feasibility of the new system is supported by a series of PSPICE simulations utilizing an electronic analogue of the proposed jerk system. The combination of features found in the new jerk system with Tchebytchev polynomials are rarely reported and thus merits dissemination.