In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential-difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit.
In this paper, we investigate the dynamical behavior in an M-dimensional nonlinear hyperchaotic model (M-NHM), where the occurrence of multistability can be observed. Four types of coexisting attractors including single limit cycle, cluster of limit cycles, single hyperchaotic attractor, and cluster of hyperchaotic attractors can be found, which are unusual behaviors in discrete chaotic systems. Furthermore, the coexistence of asymmetric and symmetric properties can be distinguished for a given set of parameters. In the endeavor of chaotification, this work introduces a simple controller on the M-NHM, which can add one more loop in each iteration, to overcome the chaos degradation in the multistability regions.
The main purpose of this paper is to introduce some new instability theorems related to certain fourth and fifth order nonlinear differential equations with a constant delay. By means of the Lyapunov-Krasovskii functional approach, we obtained two new results on the topic.
We show, contrary to expectation, that the trajectory predicted by general-relativistic mechanics for a low-speed weak-gravity system is not always well-approximated by the trajectories predicted by special-relativistic and newtonian mechanics for the same parameters and initial conditions. If the system is dissipative, the breakdown of agreement occurs for chaotic trajectories only. If the system is non-dissipative, the breakdown of agreement occurs for chaotic trajectories and non-chaotic trajectories. The agreement breaks down slowly for non-chaotic trajectories but rapidly for chaotic trajectories. When the predictions are different, general-relativistic mechanics must therefore be used, instead of special-relativistic mechanics (newtonian mechanics), to correctly study the dynamics of a weak-gravity system (a low-speed weak-gravity system).
Newtonian and special-relativistic predictions, based on the same model parameters and initial conditions for the trajectory of a low-speed scattering system are compared. When the scattering is chaotic, the two predictions for the trajectory can rapidly diverge completely, not only quantitatively but also qualitatively, due to an exponentially growing separation taking place in the scattering region. In contrast, when the scattering is nonchaotic, the breakdown of agreement between predictions takes a very long time, since the difference between the predictions grows only linearly. More importantly, in the case of low-speed chaotic scattering, the rapid loss of agreement between the Newtonian and special-relativistic trajectory predictions implies that special-relativistic mechanics must be used, instead of the standard practice of using Newtonian mechanics, to correctly describe the scattering dynamics.
The statistical predictions of Newtonian and special-relativistic mechanics, which are calculated from an initially Gaussian ensemble of trajectories, are compared for a low-speed scattering system. The comparisons are focused on the mean dwell time, transmission and reflection coefficients, and the position and momentum means and standard deviations. We find that the statistical predictions of the two theories do not always agree as conventionally expected. The predictions are close if the scattering is non-chaotic but they are radically different if the scattering is chaotic and the initial ensemble is well localized in phase space. Our result indicates that for low-speed chaotic scattering, special-relativistic mechanics must be used, instead of the standard practice of using Newtonian mechanics, to obtain empirically-correct statistical predictions from an initially well-localized Gaussian ensemble.
Data compression and encryption are key components of commonly deployed platforms such as Hadoop. Numerous data compression and encryption tools are presently available on such platforms and the tools are characteristically applied in sequence, i.e., compression followed by encryption or encryption followed by compression. This paper focuses on the open-source Hadoop framework and proposes a data storage method that efficiently couples data compression with encryption. A simultaneous compression and encryption scheme is introduced that addresses an important implementation issue of source coding based on Tent Map and Piece-wise Linear Chaotic Map (PWLM), which is the infinite precision of real numbers that result from their long products. The approach proposed here solves the implementation issue by removing fractional components that are generated by the long products of real numbers. Moreover, it incorporates a stealth key that performs a cyclic shift in PWLM without compromising compression capabilities. In addition, the proposed approach implements a masking pseudorandom keystream that enhances encryption quality. The proposed algorithm demonstrated a congruent fit within the Hadoop framework, providing robust encryption security and compression.
Although heavy-tailed fluctuations are ubiquitous in complex systems, a good understanding of the mechanisms that generate them is still lacking. Optical complex systems are ideal candidates for investigating heavy-tailed fluctuations, as they allow recording large datasets under controllable experimental conditions. A dynamical regime that has attracted a lot of attention over the years is the so-called low-frequency fluctuations (LFFs) of semiconductor lasers with optical feedback. In this regime, the laser output intensity is characterized by abrupt and apparently random dropouts. The statistical analysis of the inter-dropout-intervals (IDIs) has provided many useful insights into the underlying dynamics. However, the presence of large temporal fluctuations in the IDI sequence has not yet been investigated. Here, by applying fluctuation analysis we show that the experimental distribution of IDI fluctuations is heavy-tailed, and specifically, is well-modeled by a non-Gaussian stable distribution. We find a good qualitative agreement with simulations of the Lang-Kobayashi model. Moreover, we uncover a transition from a less-heavy-tailed state at low pump current to a more-heavy-tailed state at higher pump current. Our results indicate that fluctuation analysis can be a useful tool for investigating the output signals of complex optical systems; it can be used for detecting underlying regime shifts, for model validation and parameter estimation.
This paper proposes a generalized robust synchronization method for different dimensional fractional order dynamical systems with mismatched fractional derivatives in the presence of function uncertainty and external disturbance by a designing sliding mode controller. Based on the proposed theory of generalized robust synchronization criterion, a novel audio cryptosystem is proposed for sending or sharing voice messages secretly via insecure channel. Numerical examples are given to verify the potency of the proposed theories.
We consider a vector nonlinear differential equation of fourth order with a constant delay. We establish new sufficient conditions, which guarantee the instability of the zero solution of that equation. An example is given to illustrate the theoretical analysis made in this paper
This paper discusses the continuous effect of the fractional order parameter of the Lü system where the system response starts stable, passing by chaotic behavior then reaching periodic response as the fractional-order increases. In addition, this paper presents the concept of synchronization of different fractional order chaotic systems using active control technique. Four different synchronization cases are introduced based on the switching parameters. Also, the static and dynamic synchronizations can be obtained when the switching parameters are functions of time. The nonstandard finite difference method is used for the numerical solution of the fractional order master and slave systems. Many numeric simulations are presented to validate the concept for different fractional order parameters.
We shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a single gene with three alleles and assume that to form a new generation, each gene has a possibility to mutate, that is, to change into a gene of the other kind. We investigate the derived models and observe chaotic behaviors of such models.
The generalized and improved (G'/G)-expansion method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. In this article, we investigate the higher dimensional nonlinear evolution equation, namely, the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation via this powerful method. The solutions are found in hyperbolic, trigonometric and rational function form involving more parameters and some of our constructed solutions are identical with results obtained by other authors if certain parameters take special values and some are new. The numerical results described in the figures were obtained with the aid of commercial software Maple.
Low temperature thermal pre-treatment is a low-cost method to break down the structure of extracellular polymeric substances in waste activated sludge (WAS) while improving the sludge biodegradability. However, previous models on low temperature thermal pre-treatment did not adequately elucidate the behaviour of sludge hydrolysis process for the duration ranging from 5 to 9 h. Therefore, this work had developed an inclusive functional model to describe the kinetics of sludge hydrolysis for a wide range of treatment conditions (30 °C-90 °C within 0 and 16 h). As compared with treatment duration, the treatment temperature played a greater impact in solubilizing WAS. Accordingly, the 90 °C treatment had consistently produced WAS with the highest degree of solubility. Nonetheless, the mediocre discrepancies between 90 °C and 75 °C may challenge the practicality of increasing the treatment temperatures beyond 75 °C. The effects of treatment duration on soluble chemical oxygen demand, soluble carbohydrate and soluble protein were only significant during the first 4 h, except for humic substances release that continued to increase with treatment duration. Finally, a good fit with R2 > 0.95 was achieved using an inclusive multivariate non-linear model, substantiating the functionality to predict the kinetics of sludge hydrolysis at arbitrary treatment conditions.
In this paper, a novel, effective meta-heuristic, population-based Hybrid Firefly Particle Swarm Optimization (HFPSO) algorithm is applied to solve different non-linear and convex optimal power flow (OPF) problems. The HFPSO algorithm is a hybridization of the Firefly Optimization (FFO) and the Particle Swarm Optimization (PSO) technique, to enhance the exploration, exploitation strategies, and to speed up the convergence rate. In this work, five objective functions of OPF problems are studied to prove the strength of the proposed method: total generation cost minimization, voltage profile improvement, voltage stability enhancement, the transmission lines active power loss reductions, and the transmission lines reactive power loss reductions. The particular fitness function is chosen as a single objective based on control parameters. The proposed HFPSO technique is coded using MATLAB software and its effectiveness is tested on the standard IEEE 30-bus test system. The obtained results of the proposed algorithm are compared to simulated results of the original Particle Swarm Optimization (PSO) method and the present state-of-the-art optimization techniques. The comparison of optimum solutions reveals that the recommended method can generate optimum, feasible, global solutions with fast convergence and can also deal with the challenges and complexities of various OPF problems.
Coronary artery disease (CAD) is one of the dangerous cardiac disease, often may lead to sudden cardiac death. It is difficult to diagnose CAD by manual inspection of electrocardiogram (ECG) signals. To automate this detection task, in this study, we extracted the heart rate (HR) from the ECG signals and used them as base signal for further analysis. We then analyzed the HR signals of both normal and CAD subjects using (i) time domain, (ii) frequency domain and (iii) nonlinear techniques. The following are the nonlinear methods that were used in this work: Poincare plots, Recurrence Quantification Analysis (RQA) parameters, Shannon entropy, Approximate Entropy (ApEn), Sample Entropy (SampEn), Higher Order Spectra (HOS) methods, Detrended Fluctuation Analysis (DFA), Empirical Mode Decomposition (EMD), Cumulants, and Correlation Dimension. As a result of the analysis, we present unique recurrence, Poincare and HOS plots for normal and CAD subjects. We have also observed significant variations in the range of these features with respect to normal and CAD classes, and have presented the same in this paper. We found that the RQA parameters were higher for CAD subjects indicating more rhythm. Since the activity of CAD subjects is less, similar signal patterns repeat more frequently compared to the normal subjects. The entropy based parameters, ApEn and SampEn, are lower for CAD subjects indicating lower entropy (less activity due to impairment) for CAD. Almost all HOS parameters showed higher values for the CAD group, indicating the presence of higher frequency content in the CAD signals. Thus, our study provides a deep insight into how such nonlinear features could be exploited to effectively and reliably detect the presence of CAD.
The mechanical behavior of the heart muscle tissues is the central problem in finite element simulation of the heart contraction, excitation propagation and development of an artificial heart. Nonlinear elastic and viscoelastic passive material properties of the left ventricular papillary muscle of a guinea pig heart were determined based on in-vitro precise uniaxial and relaxation tests. The nonlinear elastic behavior was modeled by a hypoelastic model and different hyperelastic strain energy functions such as Ogden and Mooney-Rivlin. Nonlinear least square fitting and constrained optimization were conducted under MATLAB and MSC.MARC in order to obtain the model material parameters. The experimental tensile data was used to get the nonlinear elastic mechanical behavior of the heart muscle. However, stress relaxation data was used to determine the relaxation behavior as well as viscosity of the tissues. Viscohyperelastic behavior was constructed by a multiplicative decomposition of a standard Ogden strain energy function, W, for instantaneous deformation and a relaxation function, R(t), in a Prony series form. The study reveals that hypoelastic and hyperelastic (Ogden) models fit the tissue mechanical behaviors well and can be safely used for heart mechanics simulation. Since the characteristic relaxation time (900 s) of heart muscle tissues is very large compared with the actual time of heart beating cycle (800 ms), the effect of viscosity can be reasonably ignored. The amount and type of experimental data has a strong effect on the Ogden parameters. The in vitro passive mechanical properties are good initial values to start running the biosimulation codes for heart mechanics. However, an optimization algorithm is developed, based on clinical intact heart measurements, to estimate and re-correct the material parameters in order to get the in vivo mechanical properties, needed for very accurate bio-simulation and for the development of new materials for the artificial heart.
The motivation behind this paper is to seek alternative techniques to achieve a near optimal controller for non-linear systems without solving the analytical problem. In classical optimal control systems, the system states and optimization co-state parameters generate a two-point boundary value problem (TPBVP) using Pontryagin's minimum principle (PMP). The paper contributes a new fuzzy time-optimal controller to the existing fuzzy controllers which has two regular inputs and one bang-bang output. The proposed controller closely approximates the output of the classical time-optimal controller. Further, input membership function are tuned on-line to improve the time-optimal output. The new controller exhibits optimal behaviour for second order non-linear systems. The rules are selected to satisfy the stability and optimality conditions of the new fuzzy time-optimal controller. The paper describes a systematic procedure to design the controller and how to achieve the desired result. To benchmark the new controller performance, a sliding mode controller is used for guidance and comparison purpose. Simulation of three non-linear examples shows promising results. The work described here is expected to incite researcher's interest in fuzzy time-optimal controller design.
The present paper discusses the dynamics and optimal harvesting of an intraguild prey-predator fishery model by incorporating the nonlinear Michaelis-Menten type of harvesting in predator. To our knowledge, there is limited literature working on Michaelis-Menten type of harvesting in a three species intraguild model with variable carrying capacity. The carrying capacity is proportional to the density of biotic resource. The existence of the possible equilibria has been studied along with the stability criteria. We consider the impact of predator fish harvesting as the bifurcation parameter to analyze the long time behavior of the proposed system. From the economic perspective, bionomic equilibrium of the system is studied and optimal harvesting policy is derived with the assistance of Pontryagin Maximum Principle. Finally, numerical results are presented to verify our analytical results. It is shown that in the bifurcation diagrams, the system can exhibit transcritical and Hopf bifurcations in the neighborhood of coexistence equilibrium at low and relatively high level of predator harvesting respectively. Interestingly, the system enters to a bistable region where both the coexistence and predator-free equilibria can be stable depending on the initial values. This bistable behavior might be novel to the existing literature that studied intraguild models with variable carrying capacity. The objective of this study is to derive the optimal threshold for the predator harvesting that gives maximum financial profit while sustaining the fishery resources.
The present research investigates the double-chain deoxyribonucleic acid model, which is important for the transfer and retention of genetic material in biological domains. This model is composed of two lengthy uniformly elastic filaments, that stand in for a pair of polynucleotide chains of the deoxyribonucleic acid molecule joined by hydrogen bonds among the bottom combination, demonstrating the hydrogen bonds formed within the chain's base pairs. The modified extended Fan sub equation method effectively used to explain the exact travelling wave solutions for the double-chain deoxyribonucleic acid model. Compared to the earlier, now in use methods, the previously described modified extended Fan sub equation method provide more innovative, comprehensive solutions and are relatively straightforward to implement. This method transforms a non-linear partial differential equation into an ODE by using a travelling wave transformation. Additionally, the study yields both single and mixed non-degenerate Jacobi elliptic function type solutions. The complexiton, kink wave, dark or anti-bell, V, anti-Z and singular wave shapes soliton solutions are a few of the creative solutions that have been constructed utilizing modified extended Fan sub equation method that can offer details on the transversal and longitudinal moves inside the DNA helix by freely chosen parameters. Solitons propagate at a consistent rate and retain their original shape. They are widely used in nonlinear models and can be found everywhere in nature. To help in understanding the physical significance of the double-chain deoxyribonucleic acid model, several solutions are shown with graphics in the form of contour, 2D and 3D graphs using computer software Mathematica 13.2. All of the requisite constraint factors that are required for the completed solutions to exist appear to be met. Therefore, our method of strengthening symbolic computations offers a powerful and effective mathematical tool for resolving various moderate nonlinear wave problems. The findings demonstrate the system's potentially very rich precise wave forms with biological significance. The fundamentals of double-chain deoxyribonucleic acid model diffusion and processing are demonstrated by this work, which marks a substantial development in our knowledge of double-chain deoxyribonucleic acid model movements.