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The purpose of this paper is to find an exact analytical expression for the periodic solutions of the double-hump Duffing equation and an expression for the period of these solutions.

The double-hump Duffing equation is presented as a Hamiltonian system and a phase portrait of this system has been found. On the ground of analytical calculations performed using Hamiltonian-based technique, the periodic solutions of this system are represented by Jacobi elliptic functions sn, cn and dn.

Expressions for the periodic solutions and their periods of the double-hump Duffing equation have been found. An expression for the solution, in the time domain, corresponding to the heteroclinic trajectory has also been found. An important element in various applications is the relationship obtained between constant Hamiltonian levels and the elliptic modulus of the elliptic functions.

The results obtained in this paper represent a generalization and improvement of the existing ones. They can find various applications, such as analysis of limit cycles in perturbed Duffing equation, analysis of damped and forced Duffing equation, analysis of nonlinear resonance and analysis of coupled Duffing equations.

The variational principle views a complex problem in an energy way, it gives good physical understanding of an iteration method, and the variational-based numerical methods always have a conservation scheme with a fast convergent rate. The purpose of this paper is to establish a variational principle for a fractal nano/microelectromechanical (N/MEMS) system.

This paper begins with an approximate variational principle in literature for the studied problem, and a genuine variational principle is obtained by the semi-inverse method.

The semi-inverse method is a good mathematical tool to the search for a genuine fractal variational formulation for the N/MEMS system.

The established variational principle can be used for both analytical and numerical analyses of the N/MEMS systems, and it can be extended to some more complex cases.

The variational principle can be used for variational-based finite element methods and energy-based analytical methods.

The new and genuine variational principle is obtained. This paper discovers the missing piece of the puzzle for the establishment of a variational principle from governing equations for a complex problem by the semi-inverse method. The new variational theory opens a new direction in fractal MEMS systems.

The purpose of this paper is to detect the periodic signal under strong noise background, and estimate its amplitude/phase.

Melnikov method is adopted as calculating the threshold value when chaos occurs, and the detected signal is taken as a system parameter. The system's output state is changed if the parameter has a slight change near the threshold. Meantime, the phase of system's output is recognized to judge whether the output state changes, and the signal parameter is estimated according to the necessary condition.

A small periodic signal in noise can be detected by Duffing oscillator via a transition from chaotic motion to periodic motion.

The paper shows how to calculate the amplitude/phase in low signal‐to‐noise ratios.

The Duffing system is sensitive to the weak periodic signal and has definite immunity to noise, so it is easy to construct a system composed of many oscillators that could process complex signals, even though the environmental noise is intense.

This paper presents a nonlinear method for detecting and extracting the weak signal.

The purpose of this paper is to present an analytical approximate technique to solve nonlinear conservative oscillator based on the He’s energy balance method (improved version recently presented by Khan and Mirzabeigy). The method is illustrated by solving double well Duffing oscillator.

The Duffing equation with a double-well potential (with a negative linear stiffness) is an important model of a mass particle moving in a symmetric double well potential. This form of the equation also appears in the transverse vibrations of a beam when the transverse and longitudinal deflections are coupled (Thompsen, 2003).

The approximate solutions obtained by the present technique have good agreement with the numerical solution and also provide better results than other existing methods.

The results are more accurate than those obtained by other existing methods. The relative errors obtained by the present paper are less than those obtained by other existing methods. Therefore, the present technique is very effective and convenient for solving nonlinear conservative oscillator.

Embedding dimension determination in phase space reconstruction is difficult. The purpose of this paper is to present a new approach for embedding dimension determination based on empirical mode, showing that embedding dimensions for phase space reconstruction could be easily determined according to the number of intrinsic mode functions decomposed by empirical mode decomposition.

Through the relation analysis of intrinsic mode functions and embedding dimensions, the approach for embedding dimension determination by the number of intrinsic mode functions is presented. First, a time series is decomposed into several intrinsic mode functions. Second, correlation analysis between intrinsic mode functions and original signals is investigated, and then false intrinsic mode functions could be eliminated by the analysis of correlation coefficient thresholds, which makes the embedding dimension precise. Finally, the method presented is applied to the Lorenz system, Chen's system, and the Duffing equation. Simulation results prove this method is feasible.

A new approach for embedding dimension determination based on empirical mode decomposition is presented. Compared with G‐P algorithms, this new method is effective and decreases computational complexity.

This method provides an effective qualitative criterion to the selection of embedding dimensions in phase space reconstruction.

This method could be used to determine embedding dimensions of phase space reconstruction and degree‐of‐freedom of nonlinear dynamical systems.

The paper proposes a new method of embedding dimension determination in phase space reconstruction.

An iteration technique has been developed based on the Mickens iteration method to obtain approximate angular frequencies. This technique also offers the periodic solutions to the nonlinear free vibration of a conservative, coupled mass–spring system having linear and nonlinear stiffnesses with cubic nonlinearity. Two real-world cases of these systems are analysed and introduced.

In this paper, the truncated terms of the Fourier series have been used and utilized in every step of the iteration.

The obtained results are valid for whole ranges of vibration amplitude of the oscillations. The approximated results are compared with existing and corresponding numerical (considered to be exact) results which show excellent agreement. The error analysis has been carried out and shown acceptable results for the proposed iteration technique.

Effectiveness of the proposed iteration technique is found in comparison with other existing methods. The method is demonstrated by examples.

An indoor office space should not only provide adequate illuminance on horizontal planes but also cater to the physiological and psychological requirements of the occupants. This paper aims to describe a lighting simulation-based work conducted in Kolkata, India which modeled an indoor office to investigate the effects of variation in room surface reflectance combinations on user perception, mean room surface exitance (MRSE), average horizontal illuminance and overall uniformity of horizontal illuminance.

A fluorescent illumination system–based office space was modeled and retrofitted with tubular LED lamps in DIALux. Simulations were conducted for 16 different room surface reflectance combinations and a five-point Likert scale-type survey questionnaire was formulated to conduct a survey with 32 test subjects to assess the subjective preferability of each resultant light scene.

Simulation results demonstrate that the relationship between average horizontal illuminance and MRSE as well as between average horizontal illuminance and overall uniformity of horizontal illuminance, was statistically significant (p < 0.001). In the conducted survey, the resultant light scene arising out of the reflectance combination of wall:ceiling:floor = 60%:90%:20% was the most well-received one with 187 convinced agreements (“agree” and “strongly agree” responses).

This work found strong linear correlation between average horizontal illuminance and MRSE and between average horizontal illuminance and overall uniformity. A five-point Likert scale-type survey questionnaire with seven questions was formulated and validated with 32 test subjects (Cronbach’s alpha > 0.9295), which showed that the wall:ceiling:floor reflectance combination of 60%:90%:20% was the most favored choice.

An image contrast enhancement is one of the most important low‐level image pre‐processing tasks required by the vision‐based advanced driver assistance systems (ADAS). This paper seeks to address this important issue keeping the real time constraints in focus, which is especially vital for the ADAS.

The approach is based on a paradigm of nonlinear‐coupled oscillators in image processing. Each layer of the colored images is treated as an independent grayscale image and is processed separately by the paradigm. The pixels with the lowest and the highest gray levels are chosen and their difference is enhanced to span all the gray levels in an image over the entire gray level range, i.e. [0 1]. This operation enhances the contrast in each layer and the enhanced layers are finally combined to produce a color image of a much improved quality.

The approach performs robust contrast enhancement as compared to other approaches available in the relevant literature. Generally, other approaches do need a new setting of parameters for every new image to perform its task, i.e. contrast enhancement. These approaches are not useful for real‐time applications such as ADAS. Whereas, the proposed approach presented in this paper performs contrast enhancement for different images under the same setting of parameters, hence giving rise to the robustness in the system. The unique setting of parameters is derived through a bifurcation analysis explained in the paper.

The proposed approach is novel in different aspects. First, the proposed paradigm comprises of coupled differential equations, and therefore, offers a continuous model as opposed to other approaches in the relevant literature. This continuity in the model is an inherent feature of the proposed approach, which could be useful in realizing real‐time image processing with an analog implemented circuit of the approach. Furthermore, a novel framework combining coupled oscillatory paradigm and cellular neural network is also possible to achieve ultra‐fast solution in image contrast enhancement.

Good illumination creates an aesthetic environment that may positively influence patients’ well-being and provide comfort to the hospital staff. This study aims to focus on exploring the energy efficiency of lighting and subjective perception of the lit environment in a hospital ward to assess quality indicators of ambient lighting conditions.

The existing conventional tubular fluorescent lamp–based lighting system in the surveyed patients’ ward was retrofitted with light-emitting diode (LED) luminaires to explore illumination and energy parameters. Thereafter, a software lighting model was created, simulated and analyzed. A Web-based survey with five bipolar adjective pairs in a semantic differential scale was conducted with 48 participants to record and analyze their subjective responses pertaining to the variations in lamp types and surface reflectance combinations.

The findings imply that the LED tubular lamp–based illumination was deemed more adequate compared to other lamp types and the effects of variations in room surface reflectance combinations on the participants’ responses were statistically significant at α = 0.05 level. The simulated horizontal work plane average illuminance level varied from 131 to 171 lx, mean room surface exitance (MRSE) levels remained between 30 and 90 lm/m² and overall uniformity of illuminance remained between 0.5 and 0.7.

In a hospital ward illuminated by LED tubular lamps, variations in room surface reflectance combinations for a constant luminous flux package output from the lamps may affect the subjective perception of users and the correlation between horizontal work plane average illuminance and MRSE is found to be highly linear (coefficient of determination > 0.97).