A New Chaotic System with Only Nonhyperbolic Equilibrium Points: Dynamics and Its Engineering Application

In this work, we introduce a new non-Shilnikov chaotic system with an infinite number of nonhyperbolic equilibrium points. The proposed system does not have any linear term, and it is worth noting that the new system has one equilibrium point with triple zero eigenvalues at the origin. Also, the novel system has an infinite number of equilibrium points with double zero eigenvalues that are located on the z -axis. Numerical analysis of the system reveals many strong dynamics. The new system exhibits multistability and antimonotonicity. Multistability implies the coexistence of many periodic, limit cycle, and chaotic attractors under different initial values. Also, bifurcation analysis of the system shows interesting phenomena such as periodic window, period-doubling route to chaos, and inverse period-doubling bifurcations. Moreover, the complexity of the system is analyzed by computing spectral entropy. The spectral entropy distribution under different initial values is very scattered and shows that the new system has numerous multiple attractors. Finally, chaos-based encoding/decoding algorithms for secure data transmission are developed by designing a state chain diagram, which indicates the applicability of the new chaotic system.

Recursive Identification for MIMO Fractional-Order Hammerstein Model Based on AIAGS

In this paper, adaptive immune algorithm based on a global search strategy (AIAGS) and auxiliary model recursive least square method (AMRLS) are used to identify the multiple-input multiple-output fractional-order Hammerstein model. The model’s nonlinear parameters, linear parameters, and fractional order are unknown. The identification step is to use AIAGS to find the initial values of model coefficients and order at first, then bring the initial values into AMRLS to identify the coefficients and order of the model in turn. The expression of the linear block is the transfer function of the differential equation. By changing the stimulation function of the original algorithm, adopting the global search strategy before the local search strategy in the mutation operation, and adopting the parallel mechanism, AIAGS further strengthens the original algorithm’s optimization ability. The experimental results show that the proposed method is effective.

Multi-scroll fractional-order chaotic system and finite-time synchronization

The definition of fractional calculus is introduced into the 5D chaotic system, and the 5D fractional-order chaotic system is obtained. The new 5D fractional-order chaotic system has no equilibrium, multi-scroll hidden attractor and multi-stability. By analyzing the time-domain waveform, phase diagram, bifurcation diagram and complexity, it is found that the system has no equilibrium but is very sensitive to parameters and initial values. With the variation of different parameters, the system can produce attractors of different scroll types accompanied by bursting oscillation. Secondly, the multi-stability of the hidden attractor is studied. Different initial values lead to the coexistence of attractors of different scroll number, which shows the advantages of the system. The correctness and realizability of the fractional-order chaotic system are proved by analog circuit and physical implement. Finally, because of the high security of multi-scroll attractor and hidden attractor, finite-time synchronization based on the fractional-order chaotic system is studied, which has a good application prospect in the field of secure communication.

IMPACT OF DIFFERENT PRICE MOVEMENTS ON THE ACCURACY OF NUMERICAL PRICE FORECASTING

The focus of this paper aims at comparison of two prognostic numerical models with different strategies for accuracy improvement. To verify prediction performance of proposed models, the forecasts of aluminium stock exchanges on the London Metal Exchange were carried out as numerical solution of the Cauchy initial problem for the first-order ordinary differential equation. Two techniques for accuracy improvement were utilized, replacing the initial condition value by the nearest known stock exchange and a modification of the differential equation in solved Cauchy initial problem by means of two known initial values. We dealt with an idea of how different price development affected the accuracy of proposed strategies. With regard to obtained results, it was found that the prognoses obtained by using two known initial values were more increasing or decreasing than prognoses calculated by utilizing the initial condition drift. The strategy of a changing form of the differential equation in the Cauchy initial problem can be considered slightly more accurate. Faster increased prognoses were more advantageous especially at a steep price increase and within a price increase following the price decline. A moderate increase of the prognoses determined by the initial condition drift fit reasonably well a price fluctuation and a price decline following the price increase.

Noise Assisted Image Encryption and Decryption using 2-D Chaotic System

In this paper, a new two-dimensional (2-D) chaos-based color image encryption and decryption scheme is proposed in which the noise signal is selected randomly to set the initial values for a chaotic system which also enhances the security of the system. The 256-bit hash value of noise is transformed into one-time initial values for the state variables of this proposed chaotic system. XOR operation is further carried out to diffuse the pixels. Finally, statistical and security analyses are performed for understanding the effectiveness of the proposed system. Experimental results confirm that the proposed chaos-based cryptosystem is efficient and suitable for information (image) transmission in a highly secured way.

Effects of Light Pedaling Added to Contrast Water Immersion for Recovery after Exhaustive Exercise

For years, athletes and coaches have been looking for new strategies to optimize post-exercise recovery; it has recently been suggested that combining several methods might be a great option. This study therefore aimed to investigate the efficacy of contrast water therapy (CWT) used alone or associated with pedaling to recover from exhaustive exercise. After high-intensity intermittent exercise, 33 participants underwent 30 min of either (i) passive rest (PASSIVE), (ii) CWT with pedaling while in water (COMB) or (iii) classic CWT (CWT). Blood lactate concentration, countermovement jump height and perceived exhaustion were recorded before exercise, immediately after, after recovery interventions and after an additional 30 min of passive rest. Blood lactate concentration returned to initial values after 30 min of COMB (5.9 mmol/L), whereas in the other conditions even 60 min was not enough (10.2 and 9.6 mmol/L for PASSIVE and CWT, respectively, p < 0.05). Jump height was close to initial values after 30 min of CWT (37.3 cm), whereas values were still depressed after 60 min in the PASSIVE (36.0 cm) and COMB (35.7 cm) conditions (p < 0.05). Perceived exertion was still high for all conditions after 60 min. The present results are in favor of the utilization of CWT after exhaustive exercise, but the modality has to be chosen depending on what comes next (subsequent exercise scheduled in the following hours or further away).

Continuous dependence of fuzzy mild solutions on parameters for IVP of fractional fuzzy evolution equations

In this article, we are concerned with the VIP of fractional fuzzy evolution equations in the space of triangular fuzzy numbers. The continuous dependence of two kinds of fuzzy mild solutions on initial values and orders for the studied problem is obtained. The results obtained in this paper improve and extend some related conclusions on this topic.

On the Modification of Newton-Secant Method in Solving Nonlinear Equations for Multiple Zeros of Trigonometric Function

This study discusses the analysis of the modification of Newton-Secant method and solving nonlinear equations having a multiplicity of by using a modified Newton-Secant method. A nonlinear equation that has a multiplicity is an equation that has more than one root. The first step is to analyze the modification of the Newton-Secant method, namely to construct a mathematical model of the Newton-Secant method using the concept of the Newton method and the concept of the Secant method. The second step is to construct a modified mathematical model of the Newton-Secant method by adding the parameter . After obtaining the modified formula for the Newton-Secant method, then applying the method to solve a nonlinear equations that have a multiplicity . In this case, it is applied to the nonlinear equation which has a multiplicity of . The solution is done by selecting two different initial values, namely and . Furthermore, to determine the effectivity of this method, the researcher compared the result with the Newton-Raphson method, the Secant method, and the Newton-Secant method that has not been modified. The obtained results from the analysis of modification of Newton-Secant method is an iteration formula of the modified Newton-Secant method. And for the result of using a modified Newton-Secant method with two different initial values, the root of is obtained approximately, namely with less than iterations. whereas when using the Newton-Raphson method, the Secant method, and the Newton-Secant method, the root is also approximated, namely with more than iterations. Based on the problem to find the root of the nonlinear equation it can be concluded that the modified Newton-Secant method is more effective than the Newton-Raphson method, the Secant method, and the Newton-Secant method that has not been modified

Attention to principles of exercise training: an updated systematic review of randomized controlled trials in cancers other than breast and prostate

Background The primary objective of this systematic review was to update our previous review on randomized controlled trials (RCTs) of exercise in cancers other than breast or prostate, evaluating: 1) the application of principles of exercise training within the exercise prescription; 2) reporting of the exercise prescription components (i.e., frequency, intensity, time, and type (FITT)); and 3) reporting of participant adherence to FITT. A secondary objective was to examine whether reporting of these interventions had improved over time. Methods MEDLINE, EMBASE, CINAHL and SPORTDiscus databases were searched from 2012 to 2020. Eligible studies were RCTs of at least 4 weeks of aerobic and/or resistance exercise that reported on physiological outcomes relating to exercise (e.g., aerobic capacity, muscular strength) in people with cancer other than breast or prostate. Results Eighty-six new studies were identified in the updated search, for a total of 107 studies included in this review. The principle of specificity was applied by 91%, progression by 32%, overload by 46%, initial values by 72%, reversibility by 7% and diminishing returns by 5%. A significant increase in the percentage of studies that appropriately reported initial values (46 to 80%, p < 0.001) and progression (15 to 37%, p = 0.039) was found for studies published after 2011 compared to older studies. All four FITT prescription components were fully reported in the methods in 58% of all studies, which was higher than the proportion that fully reported adherence to the FITT prescription components in the results (7% of studies). Reporting of the FITT exercise prescription components and FITT adherence did not improve in studies published after 2011 compared to older studies. Conclusion Full reporting of exercise prescription and adherence still needs improvement within exercise oncology RCTs. Some aspects of exercise intervention reporting have improved since 2011, including the reporting of the principles of progression and initial values. Enhancing the reporting of exercise prescriptions, particularly FITT adherence, may provide better context for interpreting study results and improve research to practice translation.