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Traditional physics-based mathematical models of viscoelastic (VE) damper often exhibit different degrees of prediction errors under complex working conditions, whereas data-driven approaches have shown significant potential for overcoming such problems, and have not been introduced into any study to describe the dynamic mechanical properties of VE damper. In this paper, the architecture of microsphere model is adopted to represent the spatial distribution of molecular chain structure of VE damping material, which is categorized into free chains and elastic chains. Then, the physics-informed neural network surrogates are introduced to describe the statistical stress–strain behaviors of free chains and elastic chains. Finally, by constructing the physics-constrained loss function based on the combination of physics-based model and data-driven model, a physics-constrained data-driven model is proposed to characterize the dynamic mechanical behaviors of VE damper used for structure vibration control. Based on the existing experimental data, the prediction ability and robustness of the proposed model are comparatively verified, the results reveal that the proposed model can accurately reflect the stiffness and energy dissipation of VE damper under different ambient temperatures, excitation frequencies, and deformation conditions. This study proves the potential of physics-informed neural network theory in characterizing the complex mechanical behaviors of VE damper. [ABSTRACT FROM AUTHOR]

Shortage of formal jobs, lack of skills in workforce and increasing human population proliferate the informal sector. This sector provides an opportunity to unskilled workers to gain skills along with earnings. In this paper, a deterministic nonlinear mathematical model is developed to study the effects of informal skill learning and job generation on unemployment. For the formulated system, feasibility of equilibria and their stability properties are discussed. A pertinent quantity ( ℛ 0 ), known as the reproduction number, is calculated and it is shown that the formulated system undergoes transcritical, saddle-node, Hopf and Bogdanov–Takens bifurcations on the variation of ℛ 0 . The analytically obtained results are validated through numerical simulations. The results obtained from this study indicate that a substantial rate of job generation by self-employed individuals has a stabilizing effect on the system. Moreover, self-employment along with informal skill acquisition through engaging in informal work proves to be an effective measure in curbing the issue of unemployment in society. [ABSTRACT FROM AUTHOR]

The two-degree-of-freedom (2-DOF) aerial manipulator is composed of a quadrotor aircraft and a 2-DOF manipulator, which significantly expands the scope of grabbing and transporting objects. After the manipulator is installed on the quadrotor, the manipulator and the load will cause serious interference to the quadrotor, resulting in difficulty of system control and even instability. This paper presents a mathematical model of the angular velocity system of the 2-DOF aerial manipulator. The model considers the influence of the manipulator and the load on the quadrotor. Based on this model, the nonlinear dynamics of the angular velocity system of the 2-DOF aerial manipulator are analyzed by solving the equilibrium points, calculating the Lyapunov exponents, analyzing the dynamic bifurcation diagram, and drawing the dynamic region distribution map. It is found that angular velocity can produce the dynamic behaviors of sink, period-doubling, and chaos under certain circumstances. By analyzing the nonlinear dynamic behaviors of the angular velocity system under different manipulator postures, different manipulator configurations, different load masses, and different load resistances, the stability of the angular velocity system is analyzed to guide the use of the aerial manipulator more safely and efficiently. [ABSTRACT FROM AUTHOR]

Micro-Electro-Mechanical System (MEMS)-based pressure sensors operating on the principle of piezoresistivity have found profound application in various fields like automobile, aerospace, aviation, biomedical and consumer electronics. Various research studies have been conducted to optimize the design of MEMS-based pressure sensors to meet specific requirements of different fields. Modification in the structure of the piezoresistors placed on these sensors has shown great effect in this regard. However, most of these improvements have been validated through fabrication and measurement, but there has been a lack of significant studies developing analytical models to explain these improvements. This paper studies the performance of a single-turn piezoresistor design on a square silicon diaphragm. The analytical model relates the dimensions of the single-turn piezoresistor on a square diaphragm to the output voltage, and hence, sensor sensitivity is laid out. The correctness of the relation is also validated through Finite Element Analysis (FEA) performed using COMSOL Multiphysics software. Hence, an optimized single-turn design is presented which achieves a sensitivity of 203.57 mV/V/MPa over a pressure range of 0–1 MPa. These results are then compared to work from existing literature. The comparison shows an improved performance which was achieved by optimizing the design through its derived analytical model. The proposed sensor can be utilized in disposable blood pressure measurement system where high sensor sensitivity is required. [ABSTRACT FROM AUTHOR]

Replication-competent viruses have been used as an alternative therapeutic approach for cancer treatment. In this paper, a T-OV-taxis mathematical model for tumor growth with oncolytic virotherapy is established. First, the stability of u * is studied in the ODE system and in the reaction–diffusion system of the model. It is found that the stability of u * will not be changed by diffusion alone. Next, the T-OV-taxis rate χ is selected as a bifurcation factor, and a threshold value χ 0 (χ 0 < 0) is found, such that positive constant steady-state u * becomes unstable when χ < χ 0 . Hence, the taxis-driven Turing instability occurs. Furthermore, the existence, stability, turning direction of steady-state bifurcation are discussed. And, the local steady-state bifurcation is extended to a global one, where the theory used is the Crandall–Rabinowitz bifurcation theorem. Finally, it is concluded that T-OV-taxis rate χ plays an important role in this mathematical model. [ABSTRACT FROM AUTHOR]

Rectangular concrete-filled steel tubular (RCFST) columns can be designed to have unequal wall thickness to maximize their resistance to combined axial and uniaxial bending loads. However, there is very little published research on their local–global interaction buckling behavior. This paper presents an efficient fiber-based simulation model for analyzing the inelastic interaction buckling of eccentrically loaded RCFST slender columns with unequal wall thickness. The model considers the progressive local–global interaction buckling, distributed plasticity, concrete cracking and crushing, second-order effects, and geometric imperfections. The mathematical model is programmed to compute not only the axial load–displacement responses but also the interaction curves of axial load and moment of slender RCFST columns. The simulation modeling is validated by experimentally measured data. The validated computer model is used to parametrically study the interaction local–global buckling responses of RCFST columns while the range analysis is conducted to identify the relative significance of key parameters. It is demonstrated that the proposed computer model accurately simulates experimentally measured responses. Hence, it can be used with confidence in practice to analyze and design RCFST slender columns fabricated with steel plates of unequal thickness. The existing design standard AS/NZS 2327:2017 provides acceptable strength predictions of RCFST slender columns and beam-columns while the procedure specified in Eurocode 4 overestimates their capacities. [ABSTRACT FROM AUTHOR]

Children frequently experience absence seizures, a form of seizure that is characterized by brief periods of unconsciousness and staring spells. While many studies have been conducted on absence seizures, there is still some uncertainty regarding the precise mechanisms causing absence seizures. The basal ganglia are believed to be essential in regulating thalamocortical network activity responsible for such seizures. Controlling or designing a treatment for this disorder requires an understanding of the contribution of the basal ganglia regions in the absence seizures. In this regard, efforts have been made to propose a mathematical model of brain neuronal substructures and their connections in the basal ganglia. The basal ganglia cortex-thalamus (BGCT) model is one of the most-studied mathematical models investigating absence seizures. However, this model has not been comprehensively studied from the viewpoint of dynamical behavior. Hence, to evaluate the BGCT model, this paper is devoted to studying a detailed and in-depth bifurcation analysis of the basal ganglia regions in the BGCT loop. Moreover, the 0–1 test for chaos is performed to confirm the results shown in the bifurcation diagrams. Our results suggest that the BGCT model can exhibit chaotic behavior in small regions of the coupling parameter, which is consistent with the complex nature of the brain neuronal network. [ABSTRACT FROM AUTHOR]

Theoretical and computational frameworks of complexity science are dominated by binary structures. This binary bias, seen in the ubiquity of pair-wise networks and formal binary operations in mathematical models, limits our capacity to faithfully capture irreducible polyadic interactions in higher-order systems. A paradigmatic example of a higher-order interaction is the Borromean link of three interlocking rings. In this paper, we propose a mathematical framework via hypergraphs and hypermatrix algebras that allows to formalize such forms of higher-order bonding and connectivity in a parsimonious way. Our framework builds on and extends current techniques in higher-order networks — still mostly rooted in binary structures such as adjacency matrices — and incorporates recent developments in higher-arity structures to articulate the compositional behavior of adjacency hypermatrices. Irreducible higher-order interactions turn out to be a widespread occurrence across natural sciences and socio-cultural knowledge representation. We demonstrate this by reviewing recent results in computer science, physics, chemistry, biology, ecology, social science, and cultural analysis through the conceptual lens of irreducible higher-order interactions. We further speculate that the general phenomenon of emergence in complex systems may be characterized by spatio-temporal discrepancies of interaction arity. [ABSTRACT FROM AUTHOR]

In this paper, we propose a reaction–diffusion mathematical model augmented with self/cross-diffusion in 2D domain which describes the oncolytic virotherapy treatment of a tumor with its growth following the logistic law. The tumor cells are divided into uninfected and infected cells and the virus transmission is supposed to be in a direct mode (from cell to cell). In the absence of cross-diffusion, we establish well posedness of the problem, non-negativity and boundedness of solutions, nonexistence of positive solutions, local and global stability of the nontrivial steady-state and the nonoccurrence of Turing instability. In the presence of cross-diffusion, we prove the occurrence of Turing instability by using the cross-diffusion coefficient of infected cells as a parameter. To have an idea about different patterns, we derive the corresponding amplitude equation by using the nonlinear analysis theory. In the end, we perform some numerical simulations to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

The original minimum exposure path (MEP) problem in WSNs (wireless sensor networks) requires the starting point and ending point of a moving target to be fixed, thus limiting the evaluation of coverage quality relative to the locations of these points. To resolve this issue, a minimum exposure path problem with various boundaries (VB-MEP) is proposed in this paper. Because the corresponding graph model cannot be established, the original classical methods (grid method and Voronoi diagram method) used to solve the minimum exposure path problem are no longer effective for the VB-MEP problem. This paper first transforms the problem into a hybrid optimization problem with constraint conditions and then considers the characteristics of the transformed mathematical optimization model with high dimensionality, unfixed dimensionality and high nonlinearity so that the deterministic optimization methods are no longer applicable. A hybrid artificial colony solution algorithm that incorporates the actual characteristics of the problem is designed, and a convergence analysis and a proof of the designed algorithm are given. Through simulation experiments based on large-scale node distribution scenarios, it is found that the designed hybrid optimization model with constraints and hybrid artificial bee colony solution algorithm can effectively solve the proposed VB-MEP problem. [ABSTRACT FROM AUTHOR]

Side-channel attacks (SCAs) are powerful noninvasive attacks that can be used for leaking the secret key of integrated circuits (ICs). Numerous countermeasures were proposed to elevate the security level of ICs against SCAs. Unfortunately, it is quite inconvenient to predict the security levels of these countermeasures since no solid mathematical model exists in the literature. In this paper, neural network (NN)-based entropy is proposed to model the resilience of a system against SCAs. The NN-based entropy model well links the side-channel leakages and probabilities with the neurons and weights of NNs, respectively. In such a circumstance, the NN-based entropy can be used for modeling the robustness of countermeasures since a one-to-one relationship is established between the NN-based entropy and the measurement-to-disclose (MTD) enhancement ratio related with the countermeasures. As demonstrated in the result, the proposed NN-based entropy metric shows 100% consistency with the MTD enhancement ratio if multiple SCA countermeasures are employed into a system. [ABSTRACT FROM AUTHOR]

In this paper, we have studied, designed and realized a single-transistor chaotic generator with a smooth power spectrum of about −35 dBm in frequency bandwidth up to 1 GHz. The chaos generator model is described by a continuous-time six-dimensional autonomous system assuming an exponential nonlinearity. Chaotic behavior is characterized by bifurcation diagrams, Lyapunov exponents, phase portraits of the attractors and spectra of the oscillations, using both numerical and circuit simulations. Advanced Design System (ADS)-based simulations were carried out to support the theoretical analysis, and to validate the mathematical model. The simulations are carried out using real transistor parameters and taking into account the properties of the substrate, the influence of the board topology and the characteristics of the layout material. This simulation method known as EM/Circuit Co-Simulation allows the simulation results to approach as closely as possible to those of the experiments. In the light of the positive simulation results, the proposed structure is realized to demonstrate its feasibility, and to confirm the numerical results. The prototype is manufactured and mounted on a breadboard using the surface-mount devices and BFP193 bipolar junction transistor. After realizing the generator, we pushed it further towards perfection, through the proposal and realization of a broadband amplifier, in order to gain more bandwidth to improve the spectral characteristic of the generator, which makes it promising for many communication applications such as spread spectrum communication, direct chaotic communication, etc. [ABSTRACT FROM AUTHOR]

This presents a mathematical model proposed by the author for description of deformation process of a shell structure under the action of a load that depends linearly on time. Material orthotropy, geometric nonlinearity, transverse shifts are taken into account. A distinctive feature of the model is the use of a refined discrete method for taking into account stiffeners, proposed by the author earlier. Prior to this, the method was used only in static or isotropic dynamic problems. It is proposed to add correction normalizing factors, which makes it possible to obtain the most accurate values of critical loads. The methodology of the calculation algorithm under dynamic loading is based on the Kantorovich method and the Rosenbrock method, which allows solving rigid ordinary differential equation (ODE) systems. New numerical results for cylindrical panels are obtained. The influence of the number of stiffening elements on the values of the critical load is shown. A comparison with the classical discrete method of taking into account stiffeners is carried out. For the problems considered in this paper, the phase portraits of the system are shown. [ABSTRACT FROM AUTHOR]

In recent years, data-parallel computing frameworks such as Hadoop have become increasingly popular among scientists. Data-grouping-aware multiple input file data placement for Hadoop is becoming increasingly popular. However, we note that many data-grouping-aware data placement schemes for multiple input files do not take MapReduce job execution frequency into account. Through the study, such data placement schemes will increase the data transmission between nodes. The starting point of this paper is that if a certain type of MapReduce job has been executed more frequently recently, then it can be assumed that this type of job will also have a higher chance of being executed later. Based on this assumption, we proposed a data-grouping-aware multiple input files data symmetry placement method based on MapReduce jobs execution frequency (DGAMF). Based on the history of MapReduce job executions, this method first creates an inter-block join access correlation model, then divides the correlated blocks into groups according to this model and gives a mathematical model for data placement. The model can be used to guide the placement of data blocks centrally to solve the node load balancing issue caused by data asymmetry. Using the proposed method, correlated blocks from the same groups were placed in the same set of nodes, thereby effectively reducing the amount of data transmitted between nodes. Our data placement method was validated by setting up an experimental Hadoop environment. Experimental results showed that the proposed method effectively processed massive datasets and improved MapReduce's efficiency significantly. [ABSTRACT FROM AUTHOR]

Software-Defined Networking disassociates the control plane from data plane. The problem of deciding upon the number and locations of controllers and assigning switches to them has attracted the attention of researchers. Foreseeing the possibility of failure of a controller, a backup controller has to be maintained for each switch so that the switches assigned to the failed controller can immediately be connected to their backup controllers. Hence, the switches cannot experience disconnections in case of failure of their controller. In this paper, two mathematical models are proposed. The first model focuses on minimizing the average of latencies from all switches to their backup controllers while considering the failure of the controllers. The second model aims at minimizing both the average and worst-case of latencies from all switches to the corresponding backup controllers. Both of our models are evaluated on three networks and are compared (in terms of two metrics, viz., average and worst-case latencies) with an existing model that focuses on minimizing only worst-case latency. The first model gives better average latency compared to the reference model. The second model also gives better average latency and almost equal worst-case latency compared to the reference model. [ABSTRACT FROM AUTHOR]

This paper aims to utilize the modern control theory in designing an active flutter suppression controller for a two-dimensional wing with a flap. In this study, the wing's pitch–plunge linear aeroelastic response, in addition to the control flap motion, was modeled using Lagrange's energy method, and Theodorsen's classic unsteady aerodynamic theory. The derived mathematical model was represented in state-space so the modern control techniques can be implemented. The open-loop system was analyzed, and the flutter speed for a selected experimental-wing model was calculated. For model verification purposes, the open-loop simulation results were compared to an experimental study from the literature. Next, a linear quadratic Gaussian (LQG) compensator with integral action was designed and tuned using MATLAB® simulation environment to reach the best possible performance at a selected speed in the flutter region, where the results have proven excellent performance for this kind of controller in flutter suppression, as the stable flight region has successfully been extended by 29%. [ABSTRACT FROM AUTHOR]

In this paper, we have proposed a stochastic Knapsack Problem (KP) based mathematical model for small-scale vegetable sellers in India and solved it by an advanced Genetic Algorithm. The knapsack problem considered here is a bounded one, where vegetables are the objects. In this model, we have assumed that different available vegetables (objects) have different weights (that are available), purchase costs, and profits. The maximum weight of vegetables that can be transported by a seller is limited by the carrying capacity of the vegetable carrier and the business capital of the seller is also limited. The aim of the proposed mathematical model is to maximize the total profit of the loaded/traded items, with a set of predefined constraints on the part of the vegetable seller or retailer. This problem has been solved in a Type-2 fuzzy environment and the Critical Value (CV) reduction method is utilized to defuzzify the objective value. We have projected an improved genetic algorithm based approach, where we have incorporated two features, namely refinement and immigration. We have initially considered benchmark instances and subsequently some redefined cases for experimentation. Moreover, we have solved some randomly generated proposed KP instances in Type-2 fuzzy environment. [ABSTRACT FROM AUTHOR]

This paper systematically constructs a multi-project and a multi-objective human resource scheduling mathematical model in construction projects and puts forward an improved genetic algorithm to solve it by aiming at the problems existing in the process of human resource scheduling and optimization. Specifically, first, the basic mathematical models of GPRs and resource-constrained construction project human resource scheduling problem (RCWSP/GPRs) are established, and the multi-project equilibrium problem is extended. Then, an improved inter-cluster separation (ICS) algorithm is proposed and used to solve the RCWSP/GPRs problem. Finally, on this basis, the mathematical model of multi-project and multi-objective human resource scheduling problem and the solution method based on multi-objective-integrated circuit are proposed. At the same time, the resource-constrained multi-project and multi-skill human resource scheduling problem and the integer programming mathematical model under the generalized priority relationship are proposed. Also, the simulation results verify the accuracy of the proposed algorithm and model. [ABSTRACT FROM AUTHOR]

This paper analyzes the signal delay and relative stability of multilayer graphene nanoribbon (MLGNR) interconnects dependent on temperature at global lengths. A thermally aware driver interconnect load (DIL) system, constituted by equivalent single conductor (ESC) model along with mathematical equations, is proposed to convert multi-conductor transmission circuit into single transmission line of MLGNR. The temperature-dependent analytical delay model of MLGNR is evaluated and the obtained outcomes are compared with the simulated results. The analytical and simulated results are obtained at global interconnect length (2000- μ m) for 32 nm, 22 nm and 16 nm nodes of technology under 200–500 K temperature range of MLGNR. The simulation and analytical results reveal that the outcomes of the two models correspond well. The trend of the models shows the increase in delay with the rising temperature levels (200–500 K) for three different nodes of technology. Further, relative stability analysis of MLGNR as interconnect line at three different technological nodes from 500–2000- μ m lengths is examined. [ABSTRACT FROM AUTHOR]

This paper is devoted to mathematical modeling of anisotropic hyperelastic thick cylindrical shells like arteries by taking into account the volume compressibility and through-the-thickness deformation. To describe the hyperelastic behavior of this kind of shells and extract their constitutive relations, the modified anisotropic (MA) model is employed, which is able to characterize compressible behavior of hyperelastic materials like soft tissues. By considering the arterial segment as a thick cylindrical shell, the higher order thickness deformation shell theory together with nonlinear Green's strains are exploited to express its deformations and capture the thickness stretching effect. The shell is then discretized via Lagrange equations of motion to achieve the responses of the arterial wall. Numerical results are given in two sections. First, the presented formulation is validated by conducting a comparative study on a single-layer compressible pressurized shell. Close agreement between the outcomes of the developed model with those provided by finite element (FE) simulation signifies the necessity of incorporating thickness deformation in the higher order shell theory. In the next step, by considering the artery as a two-layer cylindrical shell comprising the media (the middle layer of the artery) and the adventitia (the outer layer), mechanical responses of an arterial wall subjected to an internal pressure are appraised through a number of parametric studies. [ABSTRACT FROM AUTHOR]

This paper proposes the idea of mathematical modeling of the buck converter. The modified approach is achieved through the relay feedback (RF) method and the changes are introduced on the converter output with a soft start. Mathematical modeling of the buck converter is achieved by the state-space model (SSM) and converter's transfer function (TF) to attain stability. By iteration, the proportional-integral (PI) parameters are tuned by a controller that is incorporated in the RF. The output voltage changes are introduced by maintaining the relay-tuned PI control. The concept requires small tuning times which is obtained at a reduced cost. The effectiveness of buck converter using RF is validated in simulation and hardware. [ABSTRACT FROM AUTHOR]

In this paper, a method is presented for the mathematical modeling and analysis of the DC–DC Buck Converter output voltage. This paper consists of the demonstration of a mathematical model for the converter transient response submitted to a pulse width modulated (PWM) input voltage, resulting in accurate symbolic expressions for the output voltage. The novelty of the method is the capability of the expressions derived to describe correctly the behavior of the converter submitted to time-varying control reference input signals modulating the switch pulse width. The mathematical model was then validated by comparing it with the responses obtained using the Runge–Kutta numerical method. By using different circuit parameters and PWM input signals with constant and time-varying duty cycles, it was possible to validate the model for different cases, showing the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

In this paper, considering reaction–diffusion, delay and random disturbances, two classes of mathematical models associated with Alzheimer's disease (AD) are developed. For the deterministic AD model, the stability of the unique positive equilibrium and the Hopf bifurcation are analyzed. On the other hand, focusing on the influence of uncertain factors in the environment on AD, we investigate the finite-time contractive stability (FTCS) for the stochastic AD model modulated by Markov switching process. The basic method used to formulate the FTCS of the system is the comparison method. Several illustrative examples are considered to demonstrate and verify the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the effects of offset terms on the dynamics of a modified Chua's oscillator. The mathematical model is derived using Kirchhoff's laws. The model is analyzed with the help of the maximal Lyapunov exponent, bifurcation diagrams, phase portraits, and basins of attraction. The investigations show that the offset terms break the symmetry of the system, generating more complex nonlinear phenomena like coexisting asymmetric bifurcations, coexisting asymmetric attractors, asymmetric double-scroll chaotic attractors and asymmetric attraction basins. Also, a hidden attractor (period-1 limit cycle) is found when varying the initial conditions. More interestingly, this latter attractor coexists with all other self-excited ones. A microcontroller-based implementation of the circuit is carried out to verify the numerical investigations. [ABSTRACT FROM AUTHOR]

Few studies have considered the information in the frequency domain to detect the structural breaks in financial markets. This paper provides a mixed model that integrates BEMD, AFD and Chow test to study the fluctuation characteristics of the soybean futures price. Due to the application of AFD, the mixed model can detect the structural breaks of the price fluctuation through obtaining the high-resolution information in the frequency domain. According to our results, in general, the soybean futures price in China is mainly determined by IMF11, followed by IMF9, IMF8 and IMF7, and there exist many structural breaks of different IMFs. Interestingly, national macro-controls have opposite effects at IMF8 and IMF11. The results show the effectiveness of the proposed mixed model for detecting structural breaks of financial markets in frequency-domain by revealing the impact of external events on the soybean futures price at multi-scales. [ABSTRACT FROM AUTHOR]

This paper aims to systematically study the across-wind loads of rectangular-shaped tall buildings with aerodynamic modifications and propose refined mathematic models accordingly. This study takes the CAARC (Commonwealth Advisory Aeronautical Research Council) standard tall building as a benchmark model and conducts a series of pressure measurements on the benchmark model and four CAARC models with different round corner rates (5%, 10%, 15% and 20%) in a boundary layer wind tunnel to investigate the across-wind dynamic loads of the typical tall building with different corner modifications. Based on the experimental results of the five models, base moment coefficients, power spectral densities and vertical correlation coefficients of the across-wind loads are compared and discussed. The analyzed results shown that the across-wind aerodynamic performance of the tall buildings can be effectively improved as the rounded corner rate increases. Taking the corner round rate and terrain category as two basic variables, empirical formulas for estimating the across-wind dynamic loads of CAARC standard tall buildings with various rounded corners are proposed on the basis of the wind tunnel testing results. The accuracy and applicability of the proposed formulas are verified by comparisons between the empirical formulas and the experimental results. [ABSTRACT FROM AUTHOR]

In this paper, a p53-Mdm2 mathematical model is analyzed to understand the biological implications of feedback loops in a p53 system. Results show that the model can undergo four types of codimension-3 Bogdanov–Takens bifurcations, including cusp, saddle, focus and elliptic. Specifically, we find new phenomena including the coexistence of four positive equilibria, two limit cycles, the coexistence of three stable states (two stable equilibria and one stable limit cycle, or three stable equilibria), a heteroclinic loop enclosing a smaller stable limit cycle and a larger stable limit cycle. These findings extend the understanding of the complex dynamics of the p53 system, and can provide some potential biological applications. [ABSTRACT FROM AUTHOR]

In this paper, stability of the Luo converter and the effect of circuit elements on the stability and damping fluctuation frequency is investigated. Along with this, the mathematical modeling of positive output (P/O) Luo converter in continuous conduction mode (CCM) is done by using an average state-space method. By using the obtained mathematical model, the transfer function of the Luo converter is extracted, and by using the location of the roots the mentioned transfer function, stability, and effect of circuit elements on converter behavior are studied. Also, its situations are compared with other converters. The analyses are performed through MATLAB based on simulations, which includes both roots location and bodes diagram. [ABSTRACT FROM AUTHOR]

In this paper, we explore the interplay between tumor cells and the human immune system, based on a deterministic mathematical model of minimal interactions by transforming it to stochastic model using a continuous-time Markov chain, where time is continuous but the state space is discrete. Furthermore, we simulate the stochastic basin of attraction to verify the behavior of the three critical points of interest in the deterministic system. Moreover, the stochastic simulations exemplify the cancer immunoediting theory in its three phases of development: elimination, equilibrium and escape. We extend the minimum model proposed in [DeLisi & Rescigno, 1977] to include a term of immunotherapy by lymphocyte injection, and we simulate two treatment regimes, equilibrium and escape, under several schemes. [ABSTRACT FROM AUTHOR]

In this paper, we further study a financial market model established in our earlier paper. The model dynamics is driven by a two-dimensional piecewise linear discontinuous map, which is investigated analytically and numerically for one-sided fixed points being flip saddle and two-sided fixed points being attractors. The existence of chaotic orbit is explained by using the theory of homoclinic intersection between stable and unstable manifolds of the flip saddle invariant set. The structure of chaotic attractor is disclosed. It consists of finite segments rooted on both sides of the x -axis which are unstable manifolds of flip saddle invariant set. The basins and their structural changes of bounded attractors and coexisting attractors are presented by contact bifurcation theory and numerical simulations. The border collision bifurcation (BCB for short) curves are calculated and coexisting multiattractors are disclosed by overlapping periodicity regions. The results can deepen our understanding of financial markets and dynamical systems. [ABSTRACT FROM AUTHOR]

Modern decananometer-sized MOS transistors tend to exhibit high rates of failure, underscoring the need for accurately estimating the unreliabilities of circuits built from such transistors. This paper presents a methodology for unreliability calculation that extends from individual transistors to complete logic circuits. As a logic cell's or logic circuit's unreliability is highly dependent on its transistors' drain–source and gate–source voltages, SPICE simulations are used to determine the voltages for the individual transistors. The voltage measurements are then utilized by the mathematical equations to predict the unreliabilities with high accuracy. A scalable framework based on the proposed methodology has been successfully implemented. The framework has been validated using ISCAS85 benchmark circuits. [ABSTRACT FROM AUTHOR]

Entropy is a measure of the uncertainty associated with a variable whose value cannot be exactly predicted. Based on the notion of chance measure, a concept of uncertain random entropy is introduced and used to provide a quantitative measurement of the uncertainty associated with uncertain random variables and its properties are studied in this paper. Relative entropy is a measure of the difference between two distribution functions. In order to deal with the divergence of uncertain random variables via chance distributions, this paper proposes also the relative entropy for uncertain random variables, as well as it investigates some mathematical properties of this concept. As an application, a model is presented to formulate a minimum spanning tree problem with uncertain random edge weights involving a relative entropy chance distribution. Finally, a numerical example of an uncertain random network is put forward to illustrate the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

The dynamics of the tubular chemical reactor with mass recycle was examined. In such a system, temperature and concentrations may oscillate chaotically. This means that state variable values are then unpredictable. In this paper, it has been shown that despite the chaos, the behavior of such a reactor can be predictable. It has been shown that this phenomenon can occur in two cases. The first case concerns intermittent chaos. It has been shown that intermittent outbursts can occur at regular intervals. The second case concerns transient chaos, i.e. a situation when chaos occurs only for a certain period of time, e.g. only during start-up. This phenomenon makes it impossible to predict what will occur in the reactor in the nearest time, but, makes it possible to precisely determine the values of the variables even in the distant future. Both of these phenomena were tested by numerical simulation of the mathematical model of the reactor. [ABSTRACT FROM AUTHOR]

In this work, by using an algebraic criterion presented by us in an earlier paper, we determine the conditions on the parameters in order to guarantee the nonchaotic behavior for some classes of nonlinear third-order ordinary differential equations of the form x... = j (x , ẋ , ẍ) , called jerk equations, where j is a polynomial of degree n. This kind of equation is often used in literature to study chaotic dynamics, due to its simple form and because it appears as mathematical model in several applied problems. Hence, it is an important matter to determine when it is chaotic and also nonchaotic. The results stated here, which are proved using the mentioned algebraic criterion, corroborate and extend some results already presented in literature, providing simpler proofs for the nonchaotic behavior of certain jerk equations. The algebraic criterion proved by us is quite general and can be used to study nonchaotic behavior of other types of ordinary differential equations. [ABSTRACT FROM AUTHOR]

Immunotherapy using dendritic cells (DCs) as antigen-presenting cells is widely used in laboratory and animal studies as a promising treatment for advanced prostate cancer. In this paper, the bifurcation analysis of a nonlinear model of prostate cancer with immunotherapy is performed. It is found that the model exhibits complex behaviors such as a saddle-node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation and generalized Hopf bifurcation. Moreover, it is shown that the vaccine amount and T-cells killing efficiency of tumor cells have a significant effect on tumor cells, which provides new insights to improve treatment outcomes even for patients with a weak immune system. [ABSTRACT FROM AUTHOR]

This paper describes a cholera disease transmission model in the human population through the consumption of zooplankton as food by humans. Here the plankton population is classified into two subpopulations such as phytoplankton and zooplankton. Also, human population is classified into two subpopulations such as susceptible human and infected human. The proposed system reflects the impacts of using time delay in the cholera disease transmission. Different possible equilibrium points of our proposed system have been determined. Here local and global stabilities of our proposed system have been analyzed. The existence of Hopf bifurcation has been studied at the interior equilibrium point. The normal form method and center manifold theorem have been used to test the nature of Hopf bifurcation. It is observed that the interior equilibrium is locally asymptotically stable when the time delay in disease transmission term is large, while the change of stability of positive equilibrium will cause a bifurcating periodic solution at the time delay τ to be at less than its critical value. Finally, some numerical simulation results have been presented for the better understanding of our proposed system. [ABSTRACT FROM AUTHOR]

A multistable local active meminductor emulator is proposed in this paper. The mathematical model of the emulator circuits is established. Different periodic stimuli are applied to the presented emulators and coexisting stable pinched hysteresis loops are obtained. The results obtained by experimental equips are consistent with the theoretical analysis, which indicates that the proposed emulators can work as a meminductor. [ABSTRACT FROM AUTHOR]

The differential equations used to model biological neurons and the chemical kinetics involved in synaptic excitation and inhibition have been well-established for a number of decades. For the first time, this paper presents mathematical and computational models of a neuronal binary oscillator half-adder, a neuronal Set-Reset (SR) flip-flop and a simple neuronal clocking circuit, which have all been shown to be noise resistant. In modern computers, the half-adder is the basic component to perform logic, the SR flip-flop is used to store memory and clocking circuits are used to synchronize components in parts of the computer. These novel circuits will provide the world with neuronal assays that can measure the functionality of the neurons and hence provide more information than is available with current technology. The authors are not proposing to build conventional computers with these components (they would be too slow to be practical) but the simple circuits could be used to measure the functionality of diseased circuits which are subjected to certain drugs. Neurological conditions research into Alzheimer's disease, epilepsy and Parkinson's disease, for example, would all benefit from this research. These assays for neuronal degradation could have major implications for the National Center for the Replacement, Refinement and Reduction of Animals in Research — otherwise known as the NC3R agenda. [ABSTRACT FROM AUTHOR]

Many literatures have discussed fractional order memristor and memcapacitor-based chaotic oscillators but the entire oscillator model is considered to be of fractional order. My interest is to propose a nonlinear oscillator with considering only the memcapacitor element of fractional order. Hence, I propose a fractional order memcapacitor (FMC)-based novel chaotic oscillator. The complete mathematical model for the proposed oscillator is derived and presented in this paper. The dimensionless state equations are then analyzed by using the equilibrium points and their stability, Eigen values, Kaplan–Yorke dimensions and Lyapunov exponents. To understand the complete dynamical behavior, bifurcation graphs are obtained and presented. Finally, the proposed fractional memcapacitor oscillator is implemented by using the shelf components. [ABSTRACT FROM AUTHOR]

Global analysis is often necessary for exploiting various applications or understanding the mechanisms of many dynamical phenomena in engineering practice where the underlying system model is too complex to analyze or even unavailable. Without a mathematical model, however, it is very difficult to apply cell mapping for global analysis. This paper for the first time proposes a data-driven generalized cell mapping to investigate the global properties of nonlinear systems from a sequence of measurement data, without prior knowledge of the underlying system. The proposed method includes the estimation of the state dimension of the system and time step for creating a mapping from the data. With the knowledge of the estimated state dimension and proper mapping time step, the one-step transition probability matrix can be computed from a statistical approach. The global properties of the underlying system can be uncovered with the one-step transition probability matrix. Three examples from applications are presented to illustrate a quality global analysis with the proposed data-driven generalized cell mapping method. [ABSTRACT FROM AUTHOR]

This paper presents a design and implementation of fuzzy logic controller (FLC) plus PWM sliding mode controller (SMC) for 2nd order-d KY positive output voltage boost converter (KYPOVBC) operated in continuous inductor current mode (CICM). It is more suitable for steady power source in liquid crystal display (LCD), I-pad, CCTV camera, computer parts, light emitting diode (LED), renewable energy and industrial application. The 2nd order-d KYPOVBC always works in CICM and replica of synchronous rectification characteristics. The ON/OFF nature of the 2nd order-d KYPOVBC is nonlinear and their dynamic performance becomes poor. The classical linear controllers are noncapable of output voltage regulation of this converter during the high input supply voltage and load disparities. With the purpose of improving dynamic performance, an output voltage and inductor current regulation of the 2nd order-d KYPOVBC, a SMC plus FLC is designed. The state-space equations of the 2nd order-d KYPOVBC are arrived and then, SMC parameters are calculated. The FLC rules are framed according to the working nature of the 2nd order-d KYPOVBC without mathematical modeling, which is one of the major advantages of the FLC. The SMC acts as an inside loop of this converter to regulate the inductor current, whereas the FLC and proportional integral (PI) controllers act as an outside loop of the same converter for controlling the output voltage. The performance of the designed model is investigated at various operating regions by developing both the experimental and matrix laboratory (MATLAB)/simulation link (Simulink) models in comparison with the SMC plus PI controller. The results are presented to show the best performance of the designed model. [ABSTRACT FROM AUTHOR]

In this paper, we report results related with the dynamics of two discrete-time mathematical models, which are obtained from a same continuous-time Brusselator model consisting of two nonlinear first-order ordinary differential equations. Both discrete-time mathematical models are derived by integrating the set of ordinary differential equations, but using different methods. Such results are related, in each case, with parameter-spaces of the two-dimensional map which results from the respective discretization process. The parameter-spaces obtained using both maps are then compared, and we show that the occurrence of organized periodic structures embedded in a quasiperiodic region is verified in only one of the two cases. Bifurcation diagrams, Lyapunov exponents plots, and phase-space portraits are also used, to illustrate different dynamical behaviors in both discrete-time mathematical models. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new four-dimensional hyperchaotic system derived from the chaotic maps of Peter de Jong's simple attractor and the discrete iterative function. In this work, our main motivation is to explore a link that can be developed to generate hyperchaos from 2D chaotic system. An association between 2D system and a higher order one was not studied in the previous literature. In fact, in the literature, there is no two-dimensional systems from which we are able to associate a four-dimensional one. In this context, a special interest is reserved to Peter de Jong system due to its exceptional advantages such as hypersensitivity and velocity. The challenge in this paper is the development of a four-dimensional hyperchaotic system associated to the Peter de Jong one while conserving its important characteristics such as hypersensitivity, velocity and the lack of equilibrium. The system structure that we will detail is different from other hyperchaotic systems widely suggested in the literature. In fact, the proposed attractor does not display any equilibrium point. A mathematical study is carried out in order to obtain time plots, Lyapunov exponents spectrum and bifurcation diagram. Finally, we will prove the high sensitivity of this system relative to its initial condition by simulations and experimental observations. [ABSTRACT FROM AUTHOR]

The most difficult problem of offline signature verification (SV) is that a signature is merely a static image missing a lot of the dynamic information associated with it. In this paper, three separate pseudo-dynamic features based on the gray level: gradient based local binary pattern (GLBP), statistical features of gray level co-occurrence matrix (SGLCM), simplified histogram of oriented gradients (SHOG) are proposed for writer-independent offline SV. These gray-level features can convey both texture information and the relative structural relationship of signature strokes. In addition, our experiments prove that the proposed features contain complementary information. Using random forests (RFs) as classifier, a fusion of the proposed features could achieve 7.42% and 0.08% average error rate (AER) for GPDS-253 and CEDAR datasets, respectively, which show the effectiveness of the proposed system. The implication of this paper is that part dynamic information could be extracted from a static gray level image. [ABSTRACT FROM AUTHOR]

This paper presents examples of hysteresis from a broad range of scientific disciplines and demonstrates a variety of forms including clockwise, counterclockwise, butterfly, pinched and kiss-and-go, respectively. These examples include mechanical systems made up of springs and dampers which have been the main components of muscle models for nearly one hundred years. For the first time, as far as the authors are aware, hysteresis is demonstrated in single fibre muscle when subjected to both lengthening and shortening periodic contractions. The hysteresis observed in the experiments is of two forms. Without any relaxation at the end of lengthening or shortening, the hysteresis loop is a convex clockwise loop, whereas a concave clockwise hysteresis loop (labeled as kiss-and-go) is formed when the muscle is relaxed at the end of lengthening and shortening. This paper also presents a mathematical model which reproduces the hysteresis curves in the same form as the experimental data. [ABSTRACT FROM AUTHOR]

This paper studies a mathematical model for the interaction between tumor cells and Cytotoxic T lymphocytes (CTLs) under drug therapy. We obtain some sufficient conditions for the local and global asymptotical stabilities of the system by using Schur–Cohn criterion and the theory of Lyapunov function. In addition, it is known that the system without any treatment may undergo Neimark–Sacker bifurcation, and there may exist a chaotic region of values of tumor growth rate where the system exhibits chaotic behavior. So it is important to narrow the chaotic region. This may be done by increasing the intensity of the treatment to some extent. Moreover, for a fixed value of tumor growth rate in the chaotic region, a threshold value γ 0 is predicted of the treatment parameter γ. We can see Neimark–Sacker bifurcation of the system when γ = γ 0 , and the chaotic behavior for tumor cells ends and the system becomes locally asymptotically stable when γ > γ 0 . [ABSTRACT FROM AUTHOR]

A wide variety of spatio-temporal models are available in literature which are unable to generate stationary patterns through Turing bifurcation. Introduction of nonlocal terms to the same model can produce Turing patterns and this is true even for a single species population model. In this paper, we consider a prey–predator model of Holling–Tanner type with a generalist predator and a nonlocal interaction in the intra-specific competition term of the prey population. Nonmonotonic functional response is assumed to describe consumption rate of the prey by the predator. The Turing instability condition has been studied for the model without the nonlocal term around coexisting steady states. We also determine the Turing domain in the presence of nonlocal interaction term. The spatial-Hopf bifurcation has been studied and it plays an important role to find the pure Turing domain for the nonlocal model. Furthermore, in the presence of nonlocal interaction, the nonlocal model produces traveling wave solution. Using linear stability analysis, we have obtained the wave speed for the traveling wave front analytically. With the help of numerical simulation, we have verified that the speed of the traveling wave front for the complete nonlinear nonlocal model matches with the analytical approximation. The emergence of wave trains has also been established for higher range of nonlocal interaction. [ABSTRACT FROM AUTHOR]

Weed species present high competitive capacity, rapid adaptability and herbicide resistance, hindering their effective control across worldwide cropping regions. Since field-conducted experiments are very time-consuming and usually expensive, mathematical population-based models are valuable tools to test and develop long-term weed management programs. Within this context, the objective of this paper is to formalize analytically the possible seed bank dynamics of the Lolium rigidum, subjected to different control strategies. The first focus is on studying in detail the effects of integrating constant actions, promoting more environmentally and economically sustainable scenarios. From the same perspective, an alternative to applying time-variant programs is introduced. The proposed control guarantees that the weed population is sufficiently small or, alternatively, is kept below a given economic threshold level in a ten-year planning horizon. Furthermore, an optimization criterion is adopted for distributing necessary efficiency into diverse integrated options. Numerical simulations are included to illustrate the analytical findings. [ABSTRACT FROM AUTHOR]

Manipulator robots are widely used in many fields to replace humans in complex and risky environments. However, in some particular environments the robot is prone to failure, resulting in decreased performance. In such environments, it is extremely difficult to repair the robot which interrupts the execution process. Therefore, fault tolerance plays an important role in industrial manipulators applications. In this paper, the key problems related to fault-tolerance and path planning of manipulator robots under joints failures are handled within an on-line fault-tolerant fuzzy-logic based path planning approach for high degree-of-freedom robots. This approach provides an alternative to using mathematical models to control such robots, and improves tolerance to certain faults and mechanical failures. The controller consists of two fuzzy units (i) the first unit, Fuzzy_Path_Planner, is responsible of path planning; (ii) the second unit, Fuzzy_Obstacle_Avoidance, is conceived for obstacles avoidance. Moreover, the proposed approach is capable of repelling the manipulator away from both local minima and limit cycle problems. Finally, to validate the proposed approach and show its performances and effectiveness, different tests are carried out on two six degree-of-freedom manipulator robots (ULM and PUMA560 robots), accomplishing point-to-point tasks, with and without considering some joints failures. [ABSTRACT FROM AUTHOR]

Aiming at optimizing polymer flooding, we establish an optimal control model of polymer flooding, which has an objective function of the net present value (NPV) involving the effect of polymer injection. An improved Monte Carlo gradient approximation (MCGA) algorithm, based on the idea of the ensemble-based optimization (EnOpt) scheme to solve the problem of strongly fluctuating perturbation gradients, is proposed by introducing the covariance matrix of the control vectors to filter and smooth the searching direction. A synthetic heterogeneous reservoir model is built to test the performance of the algorithms including the improved MCGA, standard MCGA and finite difference stochastic approximation (FDSA) algorithm. For the results, the improved MCGA gets closer to the optimal NPV of FDSA than the standard algorithm, and shows the high efficiency of saving calculation time compared with the FDSA. The value of NPV increases more than 20% for the improved algorithm, and the optimal production rates, injection rates, polymer concentrations, polymer slug sizes are obtained simultaneously. This paper subsequently discusses the influence of different time step sizes and oil prices. It can be concluded that moderate step size and relatively low oil price are applicable. Finally, an actual block application of the improved MCGA shows a 11.3% increase of NPV and a 6.5% increase of field oil production total (FOPT), showing the feasibility in optimizing real reservoirs. [ABSTRACT FROM AUTHOR]