Int. J. Bifurc. Chaos最新文献

{"title":"Bifurcation Structures of the Homographic γ-Ricker Maps and Their Cusp Points Organization","authors":"J. Rocha, A. Taha","doi":"10.1142/s0218127423300112","DOIUrl":"https://doi.org/10.1142/s0218127423300112","url":null,"abstract":"This paper aims to study the bifurcation structures of the homographic [Formula: see text]-Ricker maps in a four-dimensional parameter space. The generalized Lambert [Formula: see text] functions are used to establish upper bounds for the number of fixed points of these population growth models. The variation of the number of fixed points and the cusp points organization is stipulated. This study also observes a vital characteristic on the Allee effect phenomenon in a class of bimodal Allee’s maps. Some numerical studies are included to illustrate the Allee effect and big bang local bifurcations.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88635905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Effect of Dispersal Patterns on Hopf Bifurcations in a Delayed Single Population Model","authors":"Yuanyuan Zhang, D. Huang, Shanshan Chen","doi":"10.1142/s0218127423500530","DOIUrl":"https://doi.org/10.1142/s0218127423500530","url":null,"abstract":"In this paper, we consider a delayed single population model with patch structure, and investigate Hopf bifurcations when the dispersal rate or the scaling parameter of the growth rate is small. The effect of dispersal patterns is analyzed. We show that dispersal patterns affect the occurrence of Hopf bifurcations when the scaling parameter of the growth rate is small, and affect the values of Hopf bifurcations when the dispersal rate is small.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82519676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Fast Hyperchaotic Image Encryption Scheme","authors":"Xiaojuan Ma, Chunhua Wang, Wenlu Qiu, Fei Yu","doi":"10.1142/s021812742350061x","DOIUrl":"https://doi.org/10.1142/s021812742350061x","url":null,"abstract":"In this paper, we propose a fast hyperchaotic image encryption scheme based on RSVM and step-by-step scrambling-diffusion. In this scheme, we firstly propose a new algorithm named ring shrinkage with variable modulo (RSVM), which can randomly scramble the elements in a one-dimensional array, which are composed of the row numbers or column numbers of the pixel matrix to be encrypted. Before encryption, we use RSVM algorithm to generate two random one-dimensional arrays of pixel matrix (i.e. row array [Formula: see text] and column array [Formula: see text]), and each element in the [Formula: see text] represents the row/column number in the pixel matrix. Then the rows/columns of the pixel matrix are scrambled-diffused step-by-step according to the row/column numbers in the [Formula: see text]. The initial control parameters of RSVM algorithm are controlled by SHA-256 of plaintext pixels, and RSVM algorithm controls the step-by-step scrambling-diffusion process of pixel matrix, rows and columns, so the small changes of plaintext pixels will lead to great differences in ciphertext images. In addition, the overall time complexity of the image encryption scheme is only [Formula: see text], which can greatly reduce the time cost. Finally, the experimental results and extensive security analysis prove the efficiency and feasibility of this image encryption method.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85238345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamic Behavior and Double-Parameter Self-Adaptive Stability Control of a Gear Transmission System","authors":"Dongping Sheng, Fengxia Lu","doi":"10.1142/s0218127423500554","DOIUrl":"https://doi.org/10.1142/s0218127423500554","url":null,"abstract":"This paper proposes a new nonlinear transverse-torsional coupled model for single-stage gear transmission system, by taking transmission error, time-varying meshing stiffness, backlash, bearing clearances and the self-adaptive double-parameter control module into account. The nonlinear differential governing equation of system motion is derived and solved by applying variable step-size Runge–Kutta numerical integration method. The system’s nonlinear dynamic characteristics and stability are investigated systematically by a bifurcation diagram of the Poincaré map and parameter stability region. Firstly, the velocity bifurcation diagrams have shown that, under the same damping ratio and backlash and with the increase of control parameter [Formula: see text], the route to chaos in the subcritical velocity region is first experienced from crisis to periodic doubling, and to crisis again, but the route that reverts to periodic motion in the super-critical velocity region is not affected. Additionally, the backlash is found to be the key parameter to affect the route to chaos as well. With the increase of the backlash, the crisis becomes the unique route to chaos in sub-critical region no matter what the [Formula: see text] is, but the increase of [Formula: see text] could change the route that reverts to periodic motion from 3T-periodic attractor to 2T-periodic attractor. Secondly, with the increase of the control parameter [Formula: see text], the system starts to enter the chaotic motion and exit the chaos state at different critical points and through different routes. Besides, the unstable region could shrink dramatically and the route to crisis is suppressed as well with the increase of damping ratio. Thirdly, the motion stability region analysis established in full range of double-parameter and velocity provides a mathematical reference model and is stored in control module, which could be utilized to make the control module seek a nearest parameter set automatically that could make the motion stable again in the quickest way under unstable working condition. Finally, according to global motion stability diagram, the forbidden zones that cannot make the system motion stable by adjusting single control parameter are revealed, which has remarkable guiding value during the practical operation especially under the manual adjusting working condition.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78262234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence of Periodic Waves in a Perturbed Generalized BBM Equation","authors":"Yanfei Dai, Minzhi Wei, Maoan Han","doi":"10.1142/s0218127423500608","DOIUrl":"https://doi.org/10.1142/s0218127423500608","url":null,"abstract":"In this paper, a perturbed quintic BBM equation with weak backward diffusion and dissipation effects is investigated. By applying geometric singular perturbation theory and analyzing the perturbations of a Hamiltonian system with a hyper-elliptic Hamiltonian of degree six, we prove the existence of isolated periodic wave solutions with certain wave speed in an open interval. It is also shown that isolated periodic wave solutions persist for any energy parameter [Formula: see text] in an open interval under small perturbation. Furthermore, we prove that the wave speed [Formula: see text] of periodic wave is strictly monotonically increasing with respect to [Formula: see text] by analyzing Abelian integral having three generating elements. Moreover, the upper and lower bounds of the limiting wave speed are obtained. Our analysis is mainly based on Melnikov theory, Chebyshev criteria, and symbolic computation, which may be useful for other problems.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78797567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Novel Coupled Code Shifted M-ary Differential Chaos Shift Keying Modulation","authors":"Y. Wang, Hua Yang, X. Y. Yan, G. Jiang","doi":"10.1142/s0218127423500414","DOIUrl":"https://doi.org/10.1142/s0218127423500414","url":null,"abstract":"In this paper, a novel coupled code shifted M-ary differential chaos shift keying modulation scheme is proposed as a simple and low-cost solution to reference removal. In this scheme, only two information-bearing signals are transmitted. Both signals are modulated by selected Walsh code sequences with specific indices determined by the index bits, and one of them also carries an additional M-ary information symbol. Since these two information-bearing signals are coupled by the same chaotic message bearer, data bits can be easily recovered according to the correlation between these two signals so that the transmission of reference signals can be completely avoided. Theoretical Bit Error Rate (BER) expressions are derived over the additive white Gaussian noise and multipath Rayleigh fading channels. Furthermore, simulations and comparisons indicate that the proposed system can achieve better BER performance with lower complexity.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72620824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"In-Depth Analysis of Smooth and Nonsmooth Bifurcations for an Open-Loop Boost Converter Feeding Constant Power Loads in Discontinuous Conduction Mode","authors":"L. Benadero, A. E. Aroudi, L. Martínez-Salamero, C. Tse","doi":"10.1142/s0218127423500438","DOIUrl":"https://doi.org/10.1142/s0218127423500438","url":null,"abstract":"This paper presents a study of the existence conditions of limit cycles and mechanisms when losing their stability in an open-loop DC–DC boost converter loaded with a constant power load and operating in discontinuous conduction mode. First, the existence conditions are determined. Then, boundaries associated with different kinds of instabilities such as the classical smooth fold and period-doubling bifurcations and nonsmooth border-collision bifurcations such as fold border-collision bifurcations are elucidated. To perform the stability analysis, an implicit 1D map for the system is derived. From this model, it is obtained that smooth period-doubling and fold bifurcations may occur at certain values of the circuit parameters. Some results from numerical simulations performed on the circuit-based switched model are provided showing consistency with the theoretical analysis from the derived model.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85506243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Chaos and Impact Characteristics Analysis of a Multistage Planetary Gear System Based on the Energy Method","authors":"Suixian Liu, Aijun Hu, Yuyan Sun, Ling Xiang, Yancheng Zhu","doi":"10.1142/s0218127423500463","DOIUrl":"https://doi.org/10.1142/s0218127423500463","url":null,"abstract":"A dynamic modeling method for Multistage Planetary Gear Transmission (MPGT) is proposed based on the concept of integral planetary gearbox modeling. The integrated interaction of multiple nonlinear parameters is considered in the dynamic model. The time-varying mesh stiffness of each gear pair is calculated by the energy method. The effects of input torque, gear backlash, and meshing damping on the chaos and impact characteristics of the system are analyzed in detail. The results show that the dynamic behavior of the system is closely related to the Dynamic Meshing Force (DMF). When the system is in the states of chaos, bifurcation, and jumping, the DMF fluctuates violently, and the stability and reliability of the system are seriously affected. With the increase of input torque and meshing damping, the system exits chaos through the inverse period-doubling bifurcation path, which indicates that increasing the input torque and meshing damping can suppress the chaotic motion and enhance the stability of the system. The backlash has a significant effect on the nonlinear behavior and meshing impact characteristics of the system. When the backlash is small, the system is in bilateral impact, and the meshing impact tends to be stable as the backlash increases. In order to improve the vibration characteristics of the system, a slightly larger backlash is necessary. The results can be used to guide the dynamic characteristics design and vibration control of the MPGT.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85941731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Double Color Image Visual Encryption Based on Digital Chaos and Compressed Sensing","authors":"Yuxuan Sun, Lvchen Cao, Wanjun Zhang","doi":"10.1142/s021812742350044x","DOIUrl":"https://doi.org/10.1142/s021812742350044x","url":null,"abstract":"Image encryption is an effective way to protect images in secure transmission or storage. In this paper, we propose a novel double color image visual encryption algorithm based on the improved Chebyshev map (ICM) and compressed sensing. Firstly, a new nonlinear term is introduced into the classical one-dimensional Chebyshev map, and then the ICM is used to generate the secret code stream for the encryption algorithm. Next, the key-controlled sensing measurement matrices are constructed through the ICM, and they are used to compress the integer wavelet coefficients of two plain images. Subsequently, the compressed images are dislocated by dislocation matrices and diffused by an ICM-generated diffusion matrix, respectively. Finally, the encrypted images are embedded into the carrier image using the least significant bit embedding algorithm. Experimental results demonstrate that the proposed method has good visual safety, large key space, and high key sensitivity.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79130559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Novel Approach to the Characterization of Stretching and Folding in Pursuit Tracking with Chaotic and Intermittent Behaviors","authors":"F. Babazadeh, M. Ahmadi-pajouh, S. H. Golpayegani","doi":"10.1142/s0218127423500475","DOIUrl":"https://doi.org/10.1142/s0218127423500475","url":null,"abstract":"Detection of Stretching And Folding (SAF) traits in a time series is still controversial and of great interest. Also, visuo-manual tracking studies did not pay attention to SAF in hand motion trajectories. This research aims to find out the relevance of SAF to the discontinuities in chaotic dynamics of hand motion through target tracking tasks. Specifically, a new method is constructed based on this relation in which SAF can extract accurately trajectories in both time domain and phase space. Consequently, we designed experiments to track sinusoidal and trapezoidal target movements shown on a monitor. In these experiments, fourteen participants were instructed to move the joystick handle by wrist flexion-extension movements. Results confirm intermittency in significant human motor control behavior which results in discontinuities in hand motion trajectories. The relation between SAF and these discontinuities is realized by chaotic and intermittent behaviors of tracking dynamics. Verification of the method’s accuracy is also carried out by taking advantage of the Poincaré section. Our method can provide insight into the dynamical behaviors of chaotic and intermittent systems involving mechanisms in human motor control. It can be applied to general systems with intermittent behavior and other systems with modification.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73213410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}