Vol. 8, No. 3 (2024): Regular Issue

Chaotic systems have been widely adopted for image encryption as means of securely transmitting confidential information. However, literature suggests that some encryption algorithms and transmission channels may be vulnerable, which raises concerns about the efficacy of using chaotic systems for image encryption. To address these concerns, this paper proposes an approach based on dual authentication to enhance information security and mitigate image attacks. The proposed method involves encrypting the image using a secure cipher and mixing the resulting encrypted image with a chaotic signal generated by two synchronized Rössler systems before transmitting it over a channel. The original image can be recovered by reversing the encryption and transmission process. The method was successfully tested using the Mean Structural Similarity Index (MSSIM), and a second security layer showed an increase in entropy, which is a strong indicator of good random properties. The proposed scheme has been proven to be secure in encrypting and transmitting benchmark images.

One of the equations describing incognito evolution, the nonlinear Zoomeron equation, is studied in this work. In a variety of physical circumstances, including laser physics, fluid dynamics and nonlinear optics, solitons with particular properties arise and the Zoomeron equation is a single example of one such situation. The method of $\varphi^6$-model expansion allows for the explicit retrieval of a wide range of solution types, including kink-type solitons, these solitons are also called topological solitons in the context of water waves, their velocities do not depend on the wave amplitude, others are bright, singular, periodic and combined singular soliton solutions. The outcomes of this research may improve the Zoomeron equation's nonlinear dynamical features. The method proposes a practical and effective approach for solving a large class of nonlinear partial differential equations. The nonlinear dispersion behavior is analyzed for different values of the magnitude, which physically represents the wave velocity, from the parameters of the generated traveling wave solutions. Interesting graphs are employed to explain and highlight the dynamical aspects of the results, and all of the obtained results are put into the Zoomeron equation to show the accuracy of the results.

The properties of nonlinear dynamics and chaos are shown to be fundamental to optimal communication signals subject to two practical and realistic design requirements: (i) operation in a noisy environment and (ii) simple hardware implementation. The first requirement implies the receiver should include a matched filter, i.e. a filter that maximizes the signal-to-noise ratio when receiving the corresponding matched waveform. The second requirement can be met by employing a simple infinite-impulse-response (IIR) filter as the matched filter. Here we examine the waveforms matched to stable IIR filters characterized by all-pole transfer functions. This class of filters contains many of the most popular and widely used filter families, including Butterworth, Chebyshev (type I), and Bessel. We find that these waveforms are chaotic in the sense that they are deterministic and characterized by a positive Lyapunov exponent. Interestingly, a return map using samples from any such waveform takes the form of a shift map. We derive this map theoretically and present an experimental reconstruction of it using an actual electronic filter and its matched waveform. A practical consequence of chaos in these waveforms is the potential for simple and efficient signal generation using chaotic oscillators.

It is well-known that the Ginzburg-Landau equations admit at least three time-periodic solutions. One of them describes the non-super- conductive (or normal) state and the other one describes the superconductivity state. In this paper, we investigate the uniform boundedness and attractivity of these time-periodic solutions. Moreover, numerical approximations to time-periodic solutions are also presented.

As a solution to solve data congestion and improve the quality of service, edge computing emphasizes that the data of local data sources should be processed according to their locations. In order to solve the problem that the efficiency of traditional power safety management tools is low in the management cycle process that affects business delivery, this paper proposes a resource offloading algorithm with multi-access edge computing (MEC) server as the core and cloud collaborative work. Firstly, the application of MEC in the scenario of new infrastructure power safety tools is studied.Then, a three-layer edge computing architecture of terminal, edge and cloud is constructed with resource scheduling, and the attributes of incoming tasks, network transmission and computing resource performance in this scenario are dynamically considered. Finally, the fuzzy logic coordinator is used to determine which services are cached at the edge and which tasks are executed in the cloud. The simulation experiment results show that the superiority of the proposed resource offloading algorithm in the service performance of power safety tools is verified from multiple performance indexes such as service time, task failure rate, and resource utilization rate.

In this work the study and use of a continuous chaotic dynamical system with no equilibria is presented. In more details the proposed 3-D system has two hyperbolic tangent terms and it has both self excited and hidden attractors. The behavior of the system is studied numerically through phase portraits, bifurcation diagrams and Lyapunov exponents. Also, the design of a random bit generator, based on the chaotic system, is presented. The randomness of the generated bitstream is tested through NIST 800-22. Finally, the random bit generator is used in an image encryption application. The encryption scheme is resistant to various attacks, as it is thoroughly shown.

The goal of this work is to control the chaotic behavior of the passive dynamic gait of the bipedal compass walker.~An impulsive hybrid nonlinear system models the dynamic gait of the compass walker. This impulsive hybrid nature is regarded as being exceedingly complex since it has the potential to produce undesirable phenomena like chaos and bifurcations. We first demonstrate that the passive dynamic gait exhibits multiple period-doubling bifurcations that result in chaos, while altering the slope angle of the walking surface and the length of the lower leg segment. After that, in order to control chaos and achieve a one-periodic walking behavior, two controllers (a PD plus gravity compensation and an improved PD plus gravity compensation) are employed and a comparison between them is achieved. Finally, we present some simulation results demonstrating the effectiveness of the two suggested control strategies in stabilizing the chaotic passive gait of the compass-like bipedal walker.