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Physics letters. A, ISSN 0375-9601, 2008, Volume 372, Issue 4, pp. 387 - 393
This Letter introduces a new chaotic member to the three-dimensional smooth autonomous quadratic system family, which derived from the classical Lorenz system... 
Chaos | Three-scroll attractor | Lorenz attractor | Rössler attractor | BUTTERFLY ATTRACTOR | chaos | Rossler attractor | PHYSICS, MULTIDISCIPLINARY | three-scroll attractor | SYSTEMS | REALIZATION
Journal Article
International Journal of Bifurcation and Chaos, ISSN 0218-1274, 08/2017, Volume 27, Issue 9, p. 1750142
An unique 4D autonomous chaotic system with signum function term is proposed in this paper. The system has four unstable equilibria and various types of... 
butterfly attractor | circuit realization | coexisting attractors | four-scroll attractor | numerical simulation | New 4D chaotic system | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | MULTIPLE ATTRACTORS | FLOWS
Journal Article
Discrete and Continuous Dynamical Systems - Series B, ISSN 1531-3492, 05/2018, Volume 23, Issue 3, pp. 1199 - 1217
Global random attractors and random point attractors for random dynamical systems have been studied for several decades. Here we introduce two intermediate... 
Weak attractor | Random dynamical system | Hausdorff dimension | Random attractor | Forward attractor | Cc-attractor | Delta-Hausdorff-attractor | Pullback attractor | forward attractor | MATHEMATICS, APPLIED | cc-attractor | random dynamical system | SYSTEMS | weak attractor | pullback attractor
Journal Article
International Journal of Bifurcation and Chaos, ISSN 0218-1274, 04/2015, Volume 25, Issue 4, pp. 1550056 - 1-1550056-11
Discovering unknown features of no-equilibrium systems with hidden strange attractors is an attractive research topic. This paper presents a novel... 
Chaos | equilibrium | hidden attractor | multiscroll attractor | multiwing butterfly attractor | LYAPUNOV EXPONENTS | DESIGN | NUMBER | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | Strange attractors | State feedback | Construction | Methodology | Chaos theory | Bifurcations | Control systems | Butterflies
Journal Article
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, ISSN 1531-3492, 10/2019, Volume 24, Issue 10, pp. 5597 - 5600
It is well-known that random attractors of a random dynamical system are generally not unique. It was shown in [1] that if there exist more than one pullback... 
forward attractor | MATHEMATICS, APPLIED | weak attractor | Random attractor | random dynamical system | point attractor
Journal Article
2011, Mathematical surveys and monographs, ISBN 9780821868713, Volume 176, viii, 264
Book
International Journal of Bifurcation and Chaos, ISSN 0218-1274, 12/2013, Volume 23, Issue 12, pp. 1350199 - 1-1350199-10
A dynamical system with four quadratic nonlinearities is found to display a butterfly strange attractor. In a relatively large region of parameter space the... 
attraction basin | butterfly attractor | Multistability | coexisting attractor | COEXISTING ATTRACTORS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | SYSTEMS | Butterflies | Strange attractors | Basins | Fractal analysis | Nonlinearity | Fractals | Boundaries | Dynamical systems
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2009, Volume 246, Issue 2, pp. 845 - 869
The existence of a pullback attractor is established for a stochastic reaction–diffusion equation on all n-dimensional space. The nonlinearity is dissipative... 
Stochastic reaction–diffusion equation | Random attractor | Asymptotic compactness | Pullback attractor | Stochastic reaction-diffusion equation | MATHEMATICS | R-N | NAVIER-STOKES EQUATIONS | GLOBAL ATTRACTOR | LATTICE DYNAMICAL-SYSTEMS
Journal Article
The European physical journal. ST, Special topics, ISSN 1951-6401, 2017, Volume 226, Issue 9, pp. 1979 - 1985
In this paper, we describe a periodically-forced oscillator with spatially-periodic damping. This system has an infinite number of coexisting nested... 
SYSTEM | SYNCHRONIZATION | HIDDEN ATTRACTORS | SCROLL ATTRACTORS | MULTISCROLL CHAOTIC ATTRACTORS | PHYSICS, MULTIDISCIPLINARY | HYPERCHAOS TRANSITION | FLOWS | DRIVEN | MULTISTABILITY | Computer science | Islamic law | Biomedical engineering
Journal Article
Communications in nonlinear science & numerical simulation, ISSN 1007-5704, 2015, Volume 28, Issue 1-3, pp. 166 - 174
Journal Article
International Journal of Bifurcation and Chaos, ISSN 0218-1274, 02/2016, Volume 26, Issue 2, p. 1650031
Recently, many rare chaotic systems have been found including chaotic systems with no equilibria. However, it is surprising that such a system can exhibit... 
Chaos | no-equilibrium system | hidden attractor | multiscroll attractor | HIDDEN OSCILLATIONS | ATTRACTORS | SYNCHRONIZATION | DESIGN | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | FLOWS
Journal Article
Journal of Dynamics and Differential Equations, ISSN 1040-7294, 12/2018, Volume 30, Issue 4, pp. 1873 - 1898
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 07/2018, Volume 265, Issue 2, pp. 702 - 718
It is well-known that random attractors of a random dynamical system are generally not unique. We show that for general pullback attractors and weak... 
Weak attractor | Omega limit set | Compact random set | Forward attractor | Closed random set | Pullback attractor | MATHEMATICS | RANDOM DYNAMICAL-SYSTEMS
Journal Article
International Journal of Modern Physics C, ISSN 0129-1831, 06/2018, Volume 29, Issue 6, p. 1850049
Based on the simplified Lorenz multiwing attractor and the generalized Jerk multiscroll attractor, the grid compound chaotic systems are designed via state... 
Chaos | multiwing chaotic attractor | grid compound chaotic attractor | circuit implementation | multiscroll chaotic attractor | ATTRACTORS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | GENERATION | PHYSICS, MATHEMATICAL | Circuit design
Journal Article
Physics letters. A, ISSN 0375-9601, 2011, Volume 375, Issue 23, pp. 2230 - 2233
The classical attractors of Lorenz, Rossler, Chua, Chen, and other widely-known attractors are those excited from unstable equilibria. From computational point... 
Hidden attractor | Attractor localization | Experimental study | Chuaʼs circuit | Chuas circuit | HARMONIC LINEARIZATION | CHAOS | Artractor localization | PHYSICS, MULTIDISCIPLINARY | ALGORITHM | Chua's circuit | CIRCUIT | Attraction | Algorithms | Circuits | Mathematical analysis | Basins | Solid state physics | Localization | Position (location)
Journal Article
International Journal of Bifurcation and Chaos, ISSN 0218-1274, 10/2014, Volume 24, Issue 10, pp. 1450131 - 1-1450131-7
In this paper, the dynamical behavior of the Lorenz system is examined in a previously unexplored region of parameter space, in particular, where r is zero and... 
Coexisting attractor | Multistability | Lorenz system | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | EQUATIONS | multistability | MODEL | CHAOTIC ATTRACTOR | coexisting attractor | Fluids | Computational fluid dynamics | Basins | Convection modes | Fluid flow | Mathematical models | Butterflies
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2012, Volume 253, Issue 5, pp. 1544 - 1583
We study pullback attractors of non-autonomous non-compact dynamical systems generated by differential equations with non-autonomous deterministic as well as... 
Unbounded domain | Periodic random attractor | Pullback attractor | Random complete solution | REACTION-DIFFUSION EQUATIONS | MATHEMATICS | CONTINUITY | PERTURBATION | UNBOUNDED-DOMAINS | NOISE | STOCHASTIC RESONANCE
Journal Article