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Analysis of a dynamic system helps scientists understand its properties and utilize it properly in different applications. This study analyzes the effects of various external excitements on a recently proposed mathematical neuron model derived from the original Fitzhugh–Nagumo model. Different bifurcation analyses on this system are conducted to detect chaotic behaviors that are common and of great importance in biological systems, considering the effects of different types of external excitements. Lyapunov exponents (LEs) confirm the existence of chaotic patterns. Furthermore, a bifurcation diagram that looks into the changes in the system dynamics caused by the simultaneous application of the external stimulants is represented. Neurons are bound to play a role in a network in which synchrony is an analytical quality. Therefore, the potential of a network of this model in showing synchronization is examined using the master stability function (MSF) technique. Ultimately, it is concluded that this neural model can produce chaotic behaviors and synchronous networks.

Artificial intelligence has become the most widely used and trusted component of research in almost all disciplines of science and technology, starting from engineering, online businesses, and industry, to biotechnology and agriculture. Successful rice crops with maximum yield and weed management are the target set by several developed as well as developing countries, based on a combination of cultural and chemical control methods. In this paper, the weed control strategy through the competition model is documented with the aid of the time-series forecasting tool of artificial intelligence. A time-dependent computational framework is built based on the real data, and by utilizing supervised learning algorithm, incorporated with delay. It is emphasized during this research that the accurate precision of time delays in competition models can help in developing the weed control strategies more efficiently and can further support in implementing these strategies as precision models for other crop protection challenges.

In this document, Greenberg’s classical traffic model is analyzed by varying the critical velocity $v_o$ that appears in it as a parameter. This model is transformed as a discrete expression and manipulated by means of isolating variables such as vehicular density $k$, flow $q$ and velocity $v$ that appear in the model. So-called fundamental diagrams are obtained by pairing two out of these three variables, and then they are used to support trajectories of iterated processes depicting distinct behaviors of traffic. As it is shown in this paper, those behaviors have monotonous and stable patterns for some range of values of the parameter $v_o$, but they can change to cyclic and stable trajectories when this parameter is modified. If the modifications of that parameter are taken to a higher range of values, then cycles of different periods appear, reaching chaotic trajectories. These behaviors are analyzed from a dynamical approach, proving their stability conditions, and then they are illustrated with simulations in each case.

We study Brans–Dicke cosmology with an inverse power-law effective potential. By using dynamical analyses, we search for fixed points corresponding to the radiation-like matter and dark energy-dominated era of our Universe, and the stability of fixed points is also investigated. We find phase space trajectories which are attracted to the stable point of the dark energy-dominated era from unstable fixed points like matter-dominated era of the Universe. The dark energy comes from effective potentials of the Brans–Dicke field, whose variation (related to the time-variation of the gravitational coupling constant) is shown to be in good agreement with observational data.

In this paper, we investigate the cosmological dynamics in a spatially flat Friedmann–Lemaître–Robertson–Walker geometry in scalar-tensor and scalar-torsion theories where the nonminimally coupled scalar field is a complex field. We derive the cosmological field equations and we make use of dimensionless variables in order to determine the stationary points and determine their stability properties. The physical properties of the stationary points are discussed while we find that the two-different theories, scalar-tensor and scalar-torsion theories, share many common features in terms of the evolution of the physical variables in the background space.

In this paper, a dynamical model based on Kuramoto-like oscillators is used to represent the Italian high-voltage power grid. Nodes of the network are generators/substations, while links are the physical connections between generators/substations. The normal operating regime of the power grid corresponds to the regime in which the oscillations of all the nodes are synchronized. We studied the conditions for synchronization and the effect of dynamical perturbations on the nodes. The analysis allows to define several dynamical parameters assessing the dynamical robustness of the network.

Studies on fractional-order chaotic systems have increased significantly in the last decade. This paper presents Rucklidge chaotic system’s dynamical analyses and its fractional-order circuit implementations. Component values required for realizing the circuit of the fractional-order system are calculated for different fractional-orders. The feasibility of the attractor is examined by implementing its electronic circuit with a fractional-order module. The module is constructed based on the Diyi-Chen model since it is easier to implement and cost-effective. In electronic circuit implementations, it is observed that the system’s chaotic state disappears as the fractional degree decreases. Numerical and circuit simulation results are consistent well with the hardware experimental results.

A modified generalized Lorenz system in a canonical form extended from the generalized Lorenz system is proposed in this paper. This novel system has a folded factor and can display complex 2-scroll folded attractors and 1-scroll folded attractors at different parameter values. Three typical normal forms, called Lorenz-like, Chen-like and Lü-like chaotic system respectively, of three-dimensional quadratic autonomous chaotic systems are derived, and their dynamical behaviors are further investigated by employing Lyapunov exponent spectrum, bifurcation diagram, Poincaré mapping and phase portrait, etc. Of particular interest is the fact that the folded factor makes Chen-like and Lü-like chaotic systems exhibit complicated nonlinear dynamical phenomena.

It is of critical importance to comprehend the biological environment and core tumor populations when trying to design successful therapeutic solutions for fighting cancers. In several diseases, G9a has been recognized as a novel epigenetic therapeutic target, and its blockage can shift tumor cells (TCs) toward tumor propagating cells (TPCs). This study combines mathematical modeling based on ordinary differential equations and dynamical analysis to quantitatively and qualitatively understand the interactions among G9a, TCs, and TPCs, denoted as G9a-TC-TPC. We propose four different dynamical systems with the impact of the strong Allee effect, named the Hill–Hill system, Logistic–Logistic system, Hill–Logistic system and Logistic–Hill system, to simulate different biological processes through the Hill functions and the Logistic functions that are often used in the models of biological systems. Based on theoretical analysis of these models, including the positivity, boundedness and stability of equilibria, we find that the Hill–Logistic system can display bistable states that correspond to the wild-type tumors and the aggressive tumors. Consequently, we use bifurcation analysis and numerical simulations to illustrate the complicated dynamical behavior of this system. It has been shown that under a specific therapy that changes the relative apoptotic rate of TCs (G9a suppresses the apoptosis of TCs), which can affect the bistability and instability of the system, the wide-type state can be obtained. We also discover that the relative handling time of TCs and TPCs can cooperatively enhance bistability, whereas the cooperative coefficient of feedback can contribute to all tumor cells moving from high-level monostability to bistable states in a restricted region, then to low-level stable states. These results offer new insights for more precisely understanding epigenetic therapy treatments with G9a.

In this paper, a novel locally active memristor is constructed. Based on the 3D Hindmarsh–Rose (HR) and 2D FitzHugh–Nagumo (FHN) neuron, a heterogeneous neuronal system is constructed by connecting the two neurons with the locally active memristor. The equilibrium point and stability of the system are investigated. The dynamic behavior of the system is numerically and experimentally revealed by utilizing dynamic analyses in terms of interspike interval bifurcation diagram, two-parameter bifurcation diagram and so on. The unique and abundant dynamic behavior is found in the proposed neuronal system by varying the coupling strength, external stimulus current, memristive parameter and other system parameters. Multiple bursting firing groups in the tongue-shaped domains have been discovered for the first time. Finally, in order to validate the numerical simulation, an analog equivalent circuit of the heterogeneous neuronal system is devised, which demonstrates that the system is physically realizable.

We investigate the cosmological dynamics of interacting dark energy models in which the interaction function is nonlinear in terms of the energy densities. Considering explicitly the interaction between a pressureless dark matter and a scalar field, minimally coupled to Einstein gravity, we explore the dynamics of the spatially flat FLRW universe for the exponential potential of the scalar field. We perform the stability analysis for three nonlinear interaction models of our consideration through the analysis of critical points and we investigate the cosmological parameters and discuss the physical behavior at the critical points. From the analysis of the critical points we find a number of possibilities that include the stable late-time accelerated solution, $w$CDM-like solution, radiation-like solution and moreover the unstable inflationary solution.

A weakly nonlinear analysis provides a system constituting amplitude equations and its related analysis is capable of predicting parameter regimes with different patterns expected to co-exist in dynamical circumstances that exhibit complex fractional-order system characteristics. The Turing mechanism of pattern formation as a result of diffusion-induced instability of the homogeneous steady state is concerned with unpredictable conditions. The Turing instability caused by fractional diffusion in a Human Immunodeficiency Virus model has been addressed in this study. It is important that the effect of the Human Immunodeficiency Virus to the immune system can be modeled by the interaction of uninfected cells, unhealthy cells, virus particles and antigen-specific. Initially, all potential equilibrium points are defined and the stability of the interior equilibrium point is then evaluated using the Routh–Hurwitz criteria. The conditions for Turing instability are obtained by local equilibrium points with stability analysis. In the neighborhood of the Turing bifurcation point, weakly nonlinear analysis is employed to deduce the amplitude equations. After applying amplitude equations, it is observed that this system has a very rich dynamical behavior. The constraints for the formation of the patterns like a hexagon, spot, mixed and stripe patterns are identified for the amplitude equations by dynamic analysis. Furthermore, by using the numerical simulations, the theoretical results are verified. Within this framework, this study through the dynamical behavior of the complex system perspective and bifurcation point based on the viral death rate can provide the basis for several researchers working on Human Immunodeficiency Virus model through various aspects. Accordingly, the Turing bifurcation point and weakly nonlinear analysis employed within the complex fractional-order dynamics addressed herein are highly relevant experimentally since the related effects can be studied and applied concerning different mathematical, physical, engineering and biological models.

The smart wearable devices that can track the fitness activities are getting famous these days due to their easy-to-use features. The fitness trackers can work for an individual in a promising manner, provided that the user is well familiar with the device and is committed with the timelines. Several reports have provided evidence that these smart wearable devices have not showed promising results and in most of the cases, people have stopped using them, few weeks after the purchase. There are several reasons linked with this response. During this research, we have worked on the correlations of weight loss via smart device with the age, gender, body mass index (BMI) and ideal body weight (IBW), with the aid of gradient boosted decision trees (XGBoost) and support vector machine (SVM) learning tools. XGBoost and SVM are capable of dealing with complex datasets, with higher frequencies, and for data emerging from multiple sources. These machine learning tools use kernel functions for the clustering and other classification measures, and are thus better as compared to the logistic methods. Next, the time series forecasting tools are discussed with the Bayesian hyperparametric optimization. The time series of the weight loss monitoring of each individual, depicted in this manner, provided complex fractal patterns, with reduction in amplitude, with the passage of time.

In this paper, the therapeutic interactions are discussed with the aid of a mathematical model and piecewise differentiation technique. The model is based on the interaction between cell populations in therapeutic stress and cell populations in neoplastic transformation, referring specifically to triple-negative breast cancer (TNBC). The proposed computational approach provides an opportunity for the qualitative and parametric analysis of the clinical trials in question. The proposed mathematical model is based on the analysis of cell–cell interactions according to a logic that examines pathological stress and its influence on the dynamics of the cell population involved in tumor pathology. Detailed literature review and dynamical analysis of the proposed hypothesis are provided in this paper. The existence and non-negativity of the solutions are exploited, the hypothesis is stabilized; it is then further demonstrated with the aid of the piecewise derivative and the relevant application of the formula of Newton interpolation.

One of the complications caused by the viral agent SARS-CoV2 is atypical pneumonia that occurs classically in viral pathologies. These infection complications produce a sort of “cytokine release syndrome” that sees interleukin 6, a glycosylated protein of approximately 212 amino acids, among the leading players in the inflammatory process. IL-6 typically produces a transient inflammatory state that promotes the host’s immune defence through its pleiotropic function. There is the stimulation of a response in the acute infectious phase, hematopoiesis and the regular advent of immune reactions. The action of the anti-inflammatory cytokines, which tends to regulate the inflammatory one’s activity, is directed to the same cells that produce IL-6, which, through an inhibition mechanism, slow down or production ceases altogether. Evidently, in the case of the IL-6 storm, the action of these anti-inflammatory cytokines is insufficient, and the blockade of IL-6R receptors and through the use of monoclonal antibody-like tocilizumab has proved to be optimal to manage complications and avoid potentially fatal situations. Therefore, the purpose of this paper is to create a mathematical model that describes the action of the IL-6 cytokine in SARS-CoV2 virus infection to understand better the extent of the disease itself and the associated severe side effects. We represent the concentration of tocilizumab, soluble IL-6R, absolute neutrophils and circulating platelets using computational modeling. Tocilizumab is administered by intravenous infusions with a minimum dose of 80mg and a maximum dose of 400mg. Following tocilizumab administration, simulation results indicate that the population of absolute neutrophils and circulating platelets is decreasing. After the removal of tocilizumab concentration, both absolute neutrophils and circulating platelets return at their baselines.