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A 3-D four-wing attractor and its analysis

Zenghui Wang, Yanxia Sun, Barend Jacobus van Wyk, Guoyuan Qi, Michael Antonie van Wyk
2009 Brazilian journal of physics  
The new system can generate a four-wing chaotic attractor with less terms in the system equations.  ...  In this paper, several three dimensional (3-D) four-wing smooth quadratic autonomous chaotic systems are analyzed. It is shown that these systems have a number of similar features.  ...  A sine-function approach was then proposed for creating multi-scroll chaotic attractors [8] . Later, a stair function was used for generating 3D-grid-scroll attractors [9, 10] .  ... 
doi:10.1590/s0103-97332009000500007 fatcat:wfywcpmiinaxbov5gdo2gflhoe

Simulation studies on the design of optimum PID controllers to suppress chaotic oscillations in a family of Lorenz-like multi-wing attractors

Saptarshi Das, Anish Acharya, Indranil Pan
2014 Mathematics and Computers in Simulation  
Multi-wing chaotic attractors are highly complex nonlinear dynamical systems with higher number of index-2 equilibrium points.  ...  chaotic attractors.  ...  3D scroll grid attractors in [17] .  ... 
doi:10.1016/j.matcom.2014.03.002 fatcat:rxlylauwsnfopcxrjtv4fc3cja

A new type of four-wing chaotic attractors in 3-D quadratic autonomous systems

Zenghui Wang, Guoyuan Qi, Yanxia Sun, Barend Jacobus van Wyk, Michaël Antonie van Wyk
2009 Nonlinear dynamics  
These systems are derived from the existing 3-D four-wing smooth continuous autonomous chaotic systems. These new systems are the simplest chaotic attractor systems which can exhibit four wings.  ...  They have the basic structure of the existing 3-D four-wing systems, which means they can be extended to the existing 3-D fourwing chaotic systems by adding some linear and/or quadratic terms.  ...  A sine-function approach was then proposed for creating multi-scroll chaotic attractors [5] . Later, a stair function was used for generating 3D-grid-scroll attractors [6, 7] .  ... 
doi:10.1007/s11071-009-9607-8 fatcat:ka357e2p6ndynccqgskyna3zbu

On new chaotic and hyperchaotic systems: A literature survey

Abir Lassoued, Olfa Boubaker
2016 Nonlinear Analysis: Modelling and Control  
This paper provides a thorough survey of new chaotic and hyperchaotic systems.  ...  A particular classification is then proposed in this paper based on the Lyapunov exponent, the equilibriums points and the attractor forms.  ...  By replacing G(y) with a multi-piecewise square function with adjustable parameters, system (27) generates a complex grid multi-wing chaotic attractor.  ... 
doi:10.15388/na.2016.6.3 fatcat:nq5ktu3qfzghlnybkxfd6dohti

Bounded Orbits and Multiple Scroll Coexisting Attractors in a Dual System of Chua System

Yue Liu, Herbert Ho-Ching Iu, Hui Li, Xuefeng Zhang
2020 IEEE Access  
INDEX TERMS Grid multiple scroll attractors, homoclinic and heteroclinic orbits, Shilnikov bifurcation, coexisting attractors.  ...  In this paper, a method for generating M ×N ×L grid multiple scroll attractors is presented for this system.  ...  and multi-wing chaotic and hyper chaotic attractors [4] , [5] , [9] , [29] - [31] , L.  ... 
doi:10.1109/access.2020.3015865 fatcat:hzskfnfd5vffrcammt2exlsxcq

Design and Implementation of Grid Multiwing Hyperchaotic Lorenz System Family via Switching Control and Constructing Super-Heteroclinic Loops

Simin Yu, Jinhu Lu, Xinghuo Yu, Guanrong Chen
2012 IEEE Transactions on Circuits and Systems Part 1: Regular Papers  
On the other hand, the topic on generating multi-wing chaotic attractors from a 3-D smooth autonomous quadratic system deserves further detailed investigation.  ...  The four-wing chaotic attractor and its projection are shown in Figure 1 , respectively.  ... 
doi:10.1109/tcsi.2011.2180429 fatcat:prccya2gtbgadhntqmzdsiogoy


2013 Chaos, CNN, Memristors and Beyond  
This classical model exhibits the spiral and screw chaotic attractors after a period doubling cascade followed by the Shilnikov bifurcations of the saddle-focus P 2 .  ...  The diagram is built on a dense grid of 1000 × 1000 points in the (a c)-parameter plane. Solutions of the model were integrated using the high precision ODE solver TIDES [19]. The  ...  Both separatrices fill in densely two spatially symmetric, [(x, y, z) ↔ (−x, −y, z)], wings of the Lorenz attractor in the 3D phase space (see Fig. 5).  ... 
doi:10.1142/9789814434805_0033 fatcat:inw7bq2jl5htxpgnqznneryy7m

A Review of Mathematical and Computational Methods in Cancer Dynamics [article]

Abicumaran Uthamacumaran, Hector Zenil
2022 arXiv   pre-print
A class of these patterns, strange attractors, may be mathematical biomarkers of cancer progression.  ...  As such, chaotic and complex dynamics are discussed as mathematical hallmarks of cancer cell fate dynamics herein.  ...  Chaotic systems exhibit an underlying (multi)fractal topology, defined as strange attractor(s).  ... 
arXiv:2201.02055v5 fatcat:hxhvnvagcbdeldwsb3zet3wavu

Unraveling the Chaos-land and its organization in the Rabinovich System [article]

Krishna Pusuluri, Arkady Pikovsky, Andrey Shilnikov
2018 arXiv   pre-print
This suite includes Deterministic Chaos Prospector (DCP) to sweep and effectively identify regions of simple (Morse-Smale) and chaotic structurally unstable dynamics in the system.  ...  In particular, for the Lorenz-type attractors, chaotic dynamics are characterized by unpredictable flip-flop switching between the two spatial wings of the strange attractor, separated by the saddle singularity  ...  Both separatrices densely fill the two spatially symmetric wings of the Lorenz attractor in the phase space [26] .  ... 
arXiv:1806.01306v1 fatcat:naerg7d6rjg2tnlxab74wjbpca

Design and FPGA implementation of a pseudorandom number generator based on a four-wing memristive hyperchaotic system and Bernoulli map

Fei Yu, Qiuzhen Wan, Jie Jin, Lixiang Li, Binyong He, Li Liu, Shuai Qian, Yuanyuan Huang, Shuo Cai, Yun Song, Qiang Tang
2019 IEEE Access  
INDEX TERMS Pseudorandom number generator (PRNG), FPGA, four-wing memristive hyperchaotic system (FWMHS), Bernoulli map, security analysis.  ...  With the development of the theory of non-linear systems, the design of pseudorandom number generator (PRNG) for chaotic behavior of non-linear systems provides a new theoretical basis and implementation  ...  FIGURE 1 . 1 The results of FWMHS attractors obtained from Matlab: (a) x − y , (b) x − z, (c) y − z phase portraits and (d) 3D (x − y − z) chaotic phase portrait.  ... 
doi:10.1109/access.2019.2956573 fatcat:arfspl3vuredvlpvy6qkupfkbq

Dynamic Factor Graphs for Time Series Modeling [chapter]

Piotr Mirowski, Yann LeCun
2009 Lecture Notes in Computer Science  
Using smoothing regularizers, DFGs are shown to reconstruct chaotic attractors and to separate a mixture of independent oscillatory sources perfectly.  ...  Although one of the "wings" of the reconstructed butterfly-shaped attractor is slightly twisted, one can clearly distinguish two basins of attraction and a chaotic orbit switching between one and the other  ...  Fig. 5 . 5 Lorenz chaotic attractor (left) and the reconstructed chaotic attractor from the latent variables Z(t) = {z1(t), z2(t), z3(t)} after inference on the testing dataset (right).  ... 
doi:10.1007/978-3-642-04174-7_9 fatcat:xbrlv2k4qzemray4knbamcbdae


2010 Scientia Sinica Technologica  
A variety of motion types are found such as multi-periodic, quasi-periodic, and chaotic motions.  ...  Large-Eddy Simulation, Lattice Boltzmann Method, dynamics sub-grid scale model, dynamical system sub-grid scale model, parallel computation The Tsallis distribution and the stretched exponential distribution  ...  adaptive multi-grid, immersed boundary method, self-propelled swimming, fish school, 3D bionic fish Introduction The mechanics of fish swimming is an attractive research topic in fluid mechanics.  ... 
doi:10.1360/ze2010-40-3-320 fatcat:ewz7ocjff5h65ixvudgapxw43m

Lenia - Biology of Artificial Life [article]

Bert Wang-Chak Chan
2019 arXiv   pre-print
Consider the phase space trajectories of recurrent patterns (Figure 18 ), every trajectory corresponds to an attractor (or a strange attractor if chaotic).  ...  Variants and Generalizations We could also explore variants and further generalizations of Lenia, for example, higher-dimensional spaces (e.g. 3D) [72, 73, 42] ; different kinds of grids (e.g. hexagonal  ... 
arXiv:1812.05433v3 fatcat:xfnv7cb7vrhtpezkyljlsrvogi

Direct numerical simulations on the flow past a thin square plate

Yakun Zhao, Song Gao, Xiantao Zhang, Xiaoxian Guo, Xin Li, Xinliang Tian
2021 Physics of Fluids  
Different from SW mode, the multi-path butterfly like attractor as shown in Fig. 8(l) indicates that the force coefficients no longer oscillate on the exact same route.  ...  However, the sideslip angle of the low-aspect-ratio wings is usually less than 45 .  ... 
doi:10.1063/5.0039595 fatcat:dilv5ibktrehfgo4gdn3c5zrk4

Continuation of periodic solutions in the waveguide array mode-locked laser

Matthew O. Williams, Jon Wilkening, Eli Shlizerman, J. Nathan Kutz
2011 Physica D : Non-linear phenomena  
Finally, the system exhibits chaotic dynamics and transitions to the double-pulse solutions.  ...  We apply the adjoint continuation method to construct highly-accurate, periodic solutions that are observed to play a critical role in the multi-pulsing transition of mode-locked laser cavities.  ...  region in which a chaotic attractor reigns.  ... 
doi:10.1016/j.physd.2011.06.018 fatcat:vb5o6ubmonbqnavhrfuhg3kjkq
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