Pub Date : 2024-01-01DOI: 10.1142/s021812742450007x
Yikai Gao, Chunbiao Li, Irene Moroz, Haiyan Fu, Tengfei Lei
Based on the feature of piecewise linear (PWL) functions, a nonlinear feedback of a higher-order system can be transformed to an approximately equivalent PWL function so as to ease system implementation in engineering. As an example, a cubic feedback term can be approximately equivalently transformed to be a PWL function. Since the PWL function can be expressed by many simple functions such as signum function and absolute-valued function, the cubic term can be approximately equivalently replaced with these functions. Consequently, the method of approximate equivalence is employed in the JCS-08-13-2022 (JCS) chaotic system for simple circuit design and implementation. In this approach, the widely used multipliers are avoided and the circuits become more economical and also more robust. In this paper, the cubic Chua’s resistor is equivalently approximately replaced by a PWL function. To show the effectiveness of the approximate equivalence, numerical simulations are demonstrated and verified by circuit implementation.
{"title":"Approximate Equivalence of Higher-Order Feedback and Its Application in Chaotic Systems","authors":"Yikai Gao, Chunbiao Li, Irene Moroz, Haiyan Fu, Tengfei Lei","doi":"10.1142/s021812742450007x","DOIUrl":"https://doi.org/10.1142/s021812742450007x","url":null,"abstract":"Based on the feature of piecewise linear (PWL) functions, a nonlinear feedback of a higher-order system can be transformed to an approximately equivalent PWL function so as to ease system implementation in engineering. As an example, a cubic feedback term can be approximately equivalently transformed to be a PWL function. Since the PWL function can be expressed by many simple functions such as signum function and absolute-valued function, the cubic term can be approximately equivalently replaced with these functions. Consequently, the method of approximate equivalence is employed in the JCS-08-13-2022 (JCS) chaotic system for simple circuit design and implementation. In this approach, the widely used multipliers are avoided and the circuits become more economical and also more robust. In this paper, the cubic Chua’s resistor is equivalently approximately replaced by a PWL function. To show the effectiveness of the approximate equivalence, numerical simulations are demonstrated and verified by circuit implementation.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140518362","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}
Pub Date : 2024-01-01DOI: 10.1142/s0218127424500123
Huan Zhou, Xian-Feng Li, Jun Jiang, Andrew Y. T. Leung
Taking into account the nonlinear demand function, we have developed a multi-agent fishery economic model, where a multitude of agents are bounded by rationality. The fishing decisions of these agents are driven by a profit gradient mechanism. To assess the local stability of the system, stability analysis is performed with the Jury criterion. The investigation has revealed the presence of two conventional paths to chaos, namely, the flip bifurcation and the Neimark–Sacker bifurcation. This was achieved by mapping the stability regions and stability curves of the Nash equilibrium. The multistability of the system is further explored on two-dimensional planes on which the influence of joint parameters on the system’s stability is demonstrated. The existence of Arnold’s tongue has demonstrated unparalleled complexity and intricate interactions across different scales of the system. Both critical curves and basins of attraction are illustrated to gain insight into global bifurcations. The chaotic attractor is found to be confined within specific boundaries. The findings clearly show higher maximum instantaneous demand, relatively slower adjustment speed, and lower price sensitivity. Arguably, a controlled cost would lead to sustainable fishing resources. Moreover, the results also suggest that the agents would benefit more from confined conditions.
{"title":"Global Dynamics of a Fisheries Economic Model with Gradient Adjustment","authors":"Huan Zhou, Xian-Feng Li, Jun Jiang, Andrew Y. T. Leung","doi":"10.1142/s0218127424500123","DOIUrl":"https://doi.org/10.1142/s0218127424500123","url":null,"abstract":"Taking into account the nonlinear demand function, we have developed a multi-agent fishery economic model, where a multitude of agents are bounded by rationality. The fishing decisions of these agents are driven by a profit gradient mechanism. To assess the local stability of the system, stability analysis is performed with the Jury criterion. The investigation has revealed the presence of two conventional paths to chaos, namely, the flip bifurcation and the Neimark–Sacker bifurcation. This was achieved by mapping the stability regions and stability curves of the Nash equilibrium. The multistability of the system is further explored on two-dimensional planes on which the influence of joint parameters on the system’s stability is demonstrated. The existence of Arnold’s tongue has demonstrated unparalleled complexity and intricate interactions across different scales of the system. Both critical curves and basins of attraction are illustrated to gain insight into global bifurcations. The chaotic attractor is found to be confined within specific boundaries. The findings clearly show higher maximum instantaneous demand, relatively slower adjustment speed, and lower price sensitivity. Arguably, a controlled cost would lead to sustainable fishing resources. Moreover, the results also suggest that the agents would benefit more from confined conditions.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140521630","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}
Pub Date : 2024-01-01DOI: 10.1142/s0218127424500093
V. Rybin, D. Butusov, Ivan Babkin, Dmitriy Pesterev, Viacheslav Arlyapov
Various discretization effects caused by applying numerical integration techniques to continuous chaotic systems are broadly studied in nonlinear science. Along with the negative impact on the precision of the various finite-difference schemes, such effects may have surprisingly fruitful practical applications, e.g. pseudo-random number generation, image encryption with improved diffusion and confusion properties, chaotic path planning, and many others. One such application is chaos-based communication systems which gained attention in recent decades due to their high covertness and broadband transmission capability. A crucial problem in the design of chaotic communication systems is the modulation of carrier signals. Due to the noise-like properties of chaotic signals, they can barely be modulated using the same methods as conventional harmonic signals. Thus, developing new modulation techniques is of great interest in the field of chaotic communications. In this study, we investigate the discrete model of the Lorenz oscillator obtained using controllable midpoint numerical integration and develop a novel modulation technique for chaos-based communication systems. We discover and analyze the multistability phenomenon in the dynamics of the investigated finite-difference Lorenz model through bifurcation, the basin of attraction, and Lyapunov spectrum analysis procedures. Using a specially designed testbench, we explicitly show that the proposed modulation method outperforms commonly used parametric modulation and is nearly equal to the state-of-the-art symmetry-based modulation in terms of covertness and noise resistivity. In addition, the proposed modulation technique is much easier to implement using computer arithmetics, especially in fixed-point hardware. The reported results may be efficiently applied to designing advanced chaos-based communications systems or improving the characteristics of existing communication system architectures.
{"title":"Some Properties of a Discrete Lorenz System Obtained by Variable Midpoint Method and Its Application to Chaotic Signal Modulation","authors":"V. Rybin, D. Butusov, Ivan Babkin, Dmitriy Pesterev, Viacheslav Arlyapov","doi":"10.1142/s0218127424500093","DOIUrl":"https://doi.org/10.1142/s0218127424500093","url":null,"abstract":"Various discretization effects caused by applying numerical integration techniques to continuous chaotic systems are broadly studied in nonlinear science. Along with the negative impact on the precision of the various finite-difference schemes, such effects may have surprisingly fruitful practical applications, e.g. pseudo-random number generation, image encryption with improved diffusion and confusion properties, chaotic path planning, and many others. One such application is chaos-based communication systems which gained attention in recent decades due to their high covertness and broadband transmission capability. A crucial problem in the design of chaotic communication systems is the modulation of carrier signals. Due to the noise-like properties of chaotic signals, they can barely be modulated using the same methods as conventional harmonic signals. Thus, developing new modulation techniques is of great interest in the field of chaotic communications. In this study, we investigate the discrete model of the Lorenz oscillator obtained using controllable midpoint numerical integration and develop a novel modulation technique for chaos-based communication systems. We discover and analyze the multistability phenomenon in the dynamics of the investigated finite-difference Lorenz model through bifurcation, the basin of attraction, and Lyapunov spectrum analysis procedures. Using a specially designed testbench, we explicitly show that the proposed modulation method outperforms commonly used parametric modulation and is nearly equal to the state-of-the-art symmetry-based modulation in terms of covertness and noise resistivity. In addition, the proposed modulation technique is much easier to implement using computer arithmetics, especially in fixed-point hardware. The reported results may be efficiently applied to designing advanced chaos-based communications systems or improving the characteristics of existing communication system architectures.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140526365","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}
Pub Date : 2024-01-01DOI: 10.1142/s0218127424500111
Chaoxia Zhang, Shangzhou Zhang, Yuqing Zhang
This paper develops an anticontrol approach to design a 3D continuous-time autonomous chaotic system with saddle-focus homoclinic orbit, based on two chaotification criterions for all orbits to be globally bounded with positive Lyapunov exponents. By using the Shil’nikov theorem, a Poincaré return map near the origin is found in the designed controlled system, confirming the existence of chaos in sense of the Smale horseshoe.
{"title":"Generating Chaos with Saddle-Focus Homoclinic Orbit","authors":"Chaoxia Zhang, Shangzhou Zhang, Yuqing Zhang","doi":"10.1142/s0218127424500111","DOIUrl":"https://doi.org/10.1142/s0218127424500111","url":null,"abstract":"This paper develops an anticontrol approach to design a 3D continuous-time autonomous chaotic system with saddle-focus homoclinic orbit, based on two chaotification criterions for all orbits to be globally bounded with positive Lyapunov exponents. By using the Shil’nikov theorem, a Poincaré return map near the origin is found in the designed controlled system, confirming the existence of chaos in sense of the Smale horseshoe.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140524010","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}
Pub Date : 2024-01-01DOI: 10.1142/s0218127424500056
Linhe Zhu, Xinlin Chen
The harm caused by rumors is immeasurable. Studying the dynamic characteristics of rumors can help control their spread. In this paper, we propose a nonsmooth rumor model with a nonlinear propagation rate. First, we utilize the positive invariant regions to prove the boundedness of solutions. Second, we analyze the conditions for the existence of equilibrium points in both the left and right systems. Additionally, we confirm the occurrence of saddle-node bifurcation in the left system. Next, by considering the influence of spatial diffusion, we establish the conditions for Turing instability. Then we discuss the conditions for spatial homogeneous and inhomogeneous Hopf bifurcations in the left and right systems, respectively. We differentiate between supercritical and subcritical bifurcations using the Lyapunov coefficient. Furthermore, we examine the conditions for the existence of discontinuous Hopf bifurcation at the demarcation point. Finally, in the numerical simulation section, we validate our theorems on Turing patterns. We also investigate the impact of parameter changes on rumor propagation and conclude that an increase in the psychological inhibitory factor significantly reduces the rate of rumor propagation, providing an effective strategy for curbing rumors. To that end, we fit actual data to our system and the results are excellent, confirming the validity of the system.
{"title":"Modeling the Bifurcation Dynamics of Rumor Propagation in the Spatial Environment","authors":"Linhe Zhu, Xinlin Chen","doi":"10.1142/s0218127424500056","DOIUrl":"https://doi.org/10.1142/s0218127424500056","url":null,"abstract":"The harm caused by rumors is immeasurable. Studying the dynamic characteristics of rumors can help control their spread. In this paper, we propose a nonsmooth rumor model with a nonlinear propagation rate. First, we utilize the positive invariant regions to prove the boundedness of solutions. Second, we analyze the conditions for the existence of equilibrium points in both the left and right systems. Additionally, we confirm the occurrence of saddle-node bifurcation in the left system. Next, by considering the influence of spatial diffusion, we establish the conditions for Turing instability. Then we discuss the conditions for spatial homogeneous and inhomogeneous Hopf bifurcations in the left and right systems, respectively. We differentiate between supercritical and subcritical bifurcations using the Lyapunov coefficient. Furthermore, we examine the conditions for the existence of discontinuous Hopf bifurcation at the demarcation point. Finally, in the numerical simulation section, we validate our theorems on Turing patterns. We also investigate the impact of parameter changes on rumor propagation and conclude that an increase in the psychological inhibitory factor significantly reduces the rate of rumor propagation, providing an effective strategy for curbing rumors. To that end, we fit actual data to our system and the results are excellent, confirming the validity of the system.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140524626","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}
Pub Date : 2023-07-01DOI: 10.1142/s0218127423300215
Ted Szylowiec, Pawel Góra
A family of maps with memory, parameterized by [Formula: see text], is shown to have either periodic trajectories or dense trajectories on ellipses which support absolutely continuous invariant measures. Furthermore, for [Formula: see text], i.e. [Formula: see text] with [Formula: see text] and [Formula: see text], all points except [Formula: see text] either go into a polygonal region centered at [Formula: see text] if [Formula: see text] is rational, or are attracted to an elliptical region having the same center, if [Formula: see text] is irrational. In the polygonal case, we examine a mechanism for the appearance of islands supporting absolutely continuous invariant measures.
{"title":"Memory Maps with Elliptical Trajectories","authors":"Ted Szylowiec, Pawel Góra","doi":"10.1142/s0218127423300215","DOIUrl":"https://doi.org/10.1142/s0218127423300215","url":null,"abstract":"A family of maps with memory, parameterized by [Formula: see text], is shown to have either periodic trajectories or dense trajectories on ellipses which support absolutely continuous invariant measures. Furthermore, for [Formula: see text], i.e. [Formula: see text] with [Formula: see text] and [Formula: see text], all points except [Formula: see text] either go into a polygonal region centered at [Formula: see text] if [Formula: see text] is rational, or are attracted to an elliptical region having the same center, if [Formula: see text] is irrational. In the polygonal case, we examine a mechanism for the appearance of islands supporting absolutely continuous invariant measures.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74191700","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}
Pub Date : 2023-07-01DOI: 10.1142/s0218127423501110
Ruimin Liu, Minghao Liu, Tiantian Wu
Many physical and engineering systems have certain symmetric properties. Homoclinic orbits play an important role in studying the global dynamics of dynamical systems. This paper focuses on the existence and bifurcations of homoclinic orbits to a saddle in a class of three-dimensional one-parameter three-zone symmetric piecewise affine systems. Based on the analysis of the Poincaré maps, the systems have two types of limit cycles and do not have chaotic invariant sets near the homoclinic orbits. In addition, the paper provides a constant [Formula: see text] to study the homoclinic bifurcations to limit cycles for the case [Formula: see text]. Two examples with simulations of the homoclinic orbits and the limit cycles are given to illustrate the effectiveness of the results.
{"title":"Homoclinic Bifurcations in a Class of Three-Dimensional Symmetric Piecewise Affine Systems","authors":"Ruimin Liu, Minghao Liu, Tiantian Wu","doi":"10.1142/s0218127423501110","DOIUrl":"https://doi.org/10.1142/s0218127423501110","url":null,"abstract":"Many physical and engineering systems have certain symmetric properties. Homoclinic orbits play an important role in studying the global dynamics of dynamical systems. This paper focuses on the existence and bifurcations of homoclinic orbits to a saddle in a class of three-dimensional one-parameter three-zone symmetric piecewise affine systems. Based on the analysis of the Poincaré maps, the systems have two types of limit cycles and do not have chaotic invariant sets near the homoclinic orbits. In addition, the paper provides a constant [Formula: see text] to study the homoclinic bifurcations to limit cycles for the case [Formula: see text]. Two examples with simulations of the homoclinic orbits and the limit cycles are given to illustrate the effectiveness of the results.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85463618","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}
Pub Date : 2023-07-01DOI: 10.1142/s0218127423501092
S. Sriram, Hayder Natiq, K. Rajagopal, Fatemeh Parastesh, S. Jafari
Consolidation of new information in memory occurs through the simultaneous occurrence of sharp-wave ripples (SWR) in the hippocampus network, fast–slow spindles in the thalamus network, and up and down oscillations in the cortex network during sleep. Previous studies have investigated the influential and active role of spindles and sharp-wave ripples in memory consolidation. However, a detailed investigation of the effect of membrane voltage of neurons and synaptic connections between neurons in the cortex, hippocampus, and thalamus networks to create spindle and SWR is required. This paper studies the dynamic behaviors of a hippocampal-thalamic-cortical network as a function of synaptic connection between excitatory neurons, inhibitory neurons (in the hippocampus and cortex), reticular neurons, and thalamocortical neurons (in the thalamic network). The bifurcation diagrams of the hippocampus, cortex, and thalamus networks are obtained by varying the strengths of different synaptic connections. The power diagrams for SWR and sleep spindles are shown accordingly. The results show that variations in synaptic self-connection (and inhibitory synaptic connection) of excitatory neurons in the CA3 region, as well as synaptic connection between excitatory neurons from CA1 region to excitatory neurons (and inhibitory neurons) in the cortex network have the most significant influence on dynamical behavior of the network. Furthermore, comparing diagrams for different synaptic connections shows that SWR is formed by excitatory neurons in CA3 region of the hippocampal network, passes through CA1 region, and enters cortex network.
{"title":"Uncovering the Correlation Between Spindle and Ripple Dynamics and Synaptic Connections in a Hippocampal-Thalamic-Cortical Model","authors":"S. Sriram, Hayder Natiq, K. Rajagopal, Fatemeh Parastesh, S. Jafari","doi":"10.1142/s0218127423501092","DOIUrl":"https://doi.org/10.1142/s0218127423501092","url":null,"abstract":"Consolidation of new information in memory occurs through the simultaneous occurrence of sharp-wave ripples (SWR) in the hippocampus network, fast–slow spindles in the thalamus network, and up and down oscillations in the cortex network during sleep. Previous studies have investigated the influential and active role of spindles and sharp-wave ripples in memory consolidation. However, a detailed investigation of the effect of membrane voltage of neurons and synaptic connections between neurons in the cortex, hippocampus, and thalamus networks to create spindle and SWR is required. This paper studies the dynamic behaviors of a hippocampal-thalamic-cortical network as a function of synaptic connection between excitatory neurons, inhibitory neurons (in the hippocampus and cortex), reticular neurons, and thalamocortical neurons (in the thalamic network). The bifurcation diagrams of the hippocampus, cortex, and thalamus networks are obtained by varying the strengths of different synaptic connections. The power diagrams for SWR and sleep spindles are shown accordingly. The results show that variations in synaptic self-connection (and inhibitory synaptic connection) of excitatory neurons in the CA3 region, as well as synaptic connection between excitatory neurons from CA1 region to excitatory neurons (and inhibitory neurons) in the cortex network have the most significant influence on dynamical behavior of the network. Furthermore, comparing diagrams for different synaptic connections shows that SWR is formed by excitatory neurons in CA3 region of the hippocampal network, passes through CA1 region, and enters cortex network.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77259880","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}
Pub Date : 2023-07-01DOI: 10.1142/s0218127423501055
Shuai Mo, Zhen Wang, Y. Zeng, Wei Zhang
Considering the effects of time-varying meshing stiffness, time-varying support stiffness, transmission errors, tooth side clearance and bearing clearance, a nonlinear dynamics model of the coupled gear-rotor-bearing transmission system of a new energy vehicle is constructed. Firstly, the fourth-order Runge–Kutta integral method is used to solve the differential equations of the system dynamics, and the time-varying meshing force diagram, time history diagram, phase diagram, FFT spectrum diagram, Poincaré map and bifurcation diagram of the system are obtained to study the influence of the external load excitation frequency on the dynamics characteristics of the system. In addition, the multiscale method is used to analyze the main resonance characteristics of the system and to determine the main resonance stability conditions of the system. The effect of time lag control parameters and external load excitation frequency on the main resonance of the system is analyzed by numerical methods. The results show that the gear-rotor-bearing coupled transmission system of the new energy vehicle has obviously nonlinear characteristics, avoiding the system instability interval reasonable selection of external load excitation frequency, meshing damping, time lag parameters and load fluctuations, which can be used to improve the stability of the transmission system of the new energy vehicle.
{"title":"Nonlinear Vibration Analysis of the Coupled Gear-Rotor-Bearing Transmission System for a New Energy Vehicle","authors":"Shuai Mo, Zhen Wang, Y. Zeng, Wei Zhang","doi":"10.1142/s0218127423501055","DOIUrl":"https://doi.org/10.1142/s0218127423501055","url":null,"abstract":"Considering the effects of time-varying meshing stiffness, time-varying support stiffness, transmission errors, tooth side clearance and bearing clearance, a nonlinear dynamics model of the coupled gear-rotor-bearing transmission system of a new energy vehicle is constructed. Firstly, the fourth-order Runge–Kutta integral method is used to solve the differential equations of the system dynamics, and the time-varying meshing force diagram, time history diagram, phase diagram, FFT spectrum diagram, Poincaré map and bifurcation diagram of the system are obtained to study the influence of the external load excitation frequency on the dynamics characteristics of the system. In addition, the multiscale method is used to analyze the main resonance characteristics of the system and to determine the main resonance stability conditions of the system. The effect of time lag control parameters and external load excitation frequency on the main resonance of the system is analyzed by numerical methods. The results show that the gear-rotor-bearing coupled transmission system of the new energy vehicle has obviously nonlinear characteristics, avoiding the system instability interval reasonable selection of external load excitation frequency, meshing damping, time lag parameters and load fluctuations, which can be used to improve the stability of the transmission system of the new energy vehicle.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81545330","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}
Pub Date : 2023-07-01DOI: 10.1142/s0218127423501080
Jian-ming Qi, Q. Cui, Le Zhang, Yiqun Sun
Employing the Riccati–Bernoulli sub-ODE method (RBSM) and improved Weierstrass elliptic function method, we handle the proposed [Formula: see text]-dimensional nonlinear fractional electrical transmission line equation (NFETLE) system in this paper. An infinite sequence of solutions and Weierstrass elliptic function solutions may be obtained through solving the NFETLE. These new exact and solitary wave solutions are derived in the forms of trigonometric function, Weierstrass elliptic function and hyperbolic function. The graphs of soliton solutions of the NFETLE describe the dynamics of the solutions in the figures. We also discuss elaborately the effects of fraction and arbitrary parameters on a part of obtained soliton solutions which are presented graphically. Moreover, we also draw meaningful conclusions via a comparison of our partially explored areas with other different fractional derivatives. From our perspectives, by rewriting the equation as Hamiltonian system, we study the phase portrait and bifurcation of the system about NFETLE and we also for the first time discuss sensitivity of the system and chaotic behaviors. To our best knowledge, we discover a variety of new solutions that have not been reported in existing articles [Formula: see text], [Formula: see text]. The most important thing is that there are iterative ideas in finding the solution process, which have not been seen before from relevant articles such as [Tala-Tebue et al., 2014; Fendzi-Donfack et al., 2018; Ashraf et al., 2022; Ndzana et al., 2022; Halidou et al., 2022] in seeking for exact solutions about NFETLE.
本文采用riccti - bernoulli子ode方法(RBSM)和改进的Weierstrass椭圆函数方法，处理了所提出的[公式:见文]-维非线性分数阶输电线方程(NFETLE)系统。通过求解NFETLE可以得到无穷级数的解和weerstrass椭圆函数解。这些新的精确和孤立波解分别以三角函数、weerstrass椭圆函数和双曲函数的形式导出。NFETLE的孤子解的图形描述了图中解的动力学。我们还详细讨论了分数和任意参数对得到的部分孤子解的影响。此外，我们还通过比较我们部分探索的领域与其他不同的分数导数得出有意义的结论。从我们的角度出发，通过将方程改写为哈密顿系统，我们研究了NFETLE系统的相画像和分岔，并首次讨论了系统的灵敏度和混沌行为。据我们所知，我们发现了现有文章中没有报道的各种新的解决方案[公式:见文本]，[公式:见文本]。最重要的是，在寻找解决方案的过程中有迭代的想法，这在之前的相关文章中没有见过，如[Tala-Tebue et al.， 2014;Fendzi-Donfack et al.， 2018;Ashraf et al.， 2022;Ndzana et al.， 2022;Halidou et al.， 2022]寻求NFETLE的精确解。
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