Deterministic nonperiodic flow, Journal of the Atmospheric Sciences, vol.20, issue.2, pp.130-141, 1963. ,
DOI : 10.1201/9780203734636-38
, Qualitative Theory of Differential Equations, 1989.
A Strange, Strange attractor, in the Hopf bifurcation and its application, Applied Mathematical Series, vol.19, pp.368-381, 1976. ,
The origin and structure of the Lorenz attractor, Soviet Physics Doklady, vol.22, pp.253-255, 1977. ,
, The structure of Lorenz attractors, Publications mathématiques de l'IHÉSIH´IHÉS, vol.50, pp.321-347, 1979.
Preturbulence: a regime observed in a fluid flow model of Lorenz, Communications in Mathematical Physics, vol.6, issue.2, pp.93-108, 1979. ,
The Rikitake two-disc dynamo system, Mathematical Proceedings of the Cambridge Philosophical Society, vol.68, pp.547-569, 1970. ,
DOI : 10.1017/s0305004100046338
On the appearance of chaos in a model of the Belousov reaction, Journal of Mathematical Biology, vol.5, issue.4, pp.351-362, 1977. ,
El Niño: A chaotic dynamical system?, Science, vol.232, issue.4747, pp.243-245, 1986. ,
Conceptual models of El Niño and the Southern Oscillation, Journal of Geophysical Research, vol.93, issue.C11, pp.13979-13991, 1988. ,
Some simple chaotic flows, Physical Review E, vol.50, issue.2, p.647, 1994. ,
DOI : 10.1103/physreve.50.r647
Simplest dissipative chaotic flow, Physics Letters A, vol.228, issue.4-5, pp.271-274, 1997. ,
Dynamical behaviors of a chaotic system with no equilibria, Physics Letters A, vol.376, issue.2, pp.102-108, 2011. ,
A chaotic system with only one stable equilibrium, Communications in Nonlinear Science and Numerical Simulation, vol.17, issue.3, pp.1264-1272, 2012. ,
Generalized Lorenz equations for acoustic-gravity waves in the atmosphere, Physica Scripta, vol.53, issue.1, pp.83-84, 1996. ,
Yet another chaotic attractor, International Journal of Bifurcation and Chaos, vol.9, issue.7, pp.1465-1466, 1999. ,
Bifurcation analysis of Chen's equation, International Journal of Bifurcation and Chaos, vol.10, issue.8, pp.1917-1931, 2000. ,
, New Methods for Chaotic Dynamics, 2006.
, Sequential memory: binding dynamics, p.103118, 2015.
, Heteroclinic binding, vol.25, pp.433-442, 2010.
Hidden attractors in dynamical systems, Physics Reports, vol.637, issue.3, pp.1-50, 2016. ,
Metastable chaos: the transition to sustained chaotic behavior in the Lorenz model, Journal of Statistical Physics, vol.21, issue.3, pp.263-277, 1979. ,
Computed chaos or numerical errors, Nonlinear Analysis: Modelling and Control, vol.15, pp.109-126, 2010. ,
, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors, 1982.
Search for and stabilization of unstable saddle cycles in the Lorenz system, Differential Equations, vol.37, pp.1636-1639, 2001. ,
On the numerical solution of chaotic dynamical systems using extend precision floating point arithmetic and very high order numerical methods, Nonlinear Analysis: Modelling and Control, vol.16, issue.3, pp.340-352, 2011. ,
Predictability: does the flap of a butterfly's wings in Brazil set off a tornado in Texas?, 139th Meeting. AAAS Section on Environmental Sciences New Approaches to Global Weather: GARP (The Global Atmospheric Research Program), 1972. ,
A new piecewise-quasilinearization method for solving chaotic systems of initial value problems, Central European Journal of Physics, vol.10, issue.4, pp.936-946, 2012. ,
A new multistage spectral relaxation method for solving chaotic initial value systems, Nonlinear Dynamics, vol.72, issue.1, pp.265-283, 2013. ,
Numerical simulation of chaotic dynamical systems by the method of differential quadrature, Scientia Iranica B, vol.19, issue.5, pp.1299-1315, 2012. ,
The multistage homotopy-perturbation method: a powerful scheme for handling the Lorenz system, Chaos, Solitons and Fractals, vol.40, issue.4, pp.1929-1937, 2009. ,
A program for the automatic integration of differential equations using the method of Taylor series, The Computer Journal, vol.3, issue.2, pp.108-111, 1960. ,
, Automatic Differentiation: Techniques and Applications, 1981.
Accuracy of the Adomian decomposition method applied to the Lorenz system, Chaos, Solitons and Fractals, vol.28, issue.5, pp.1149-1158, 2006. ,
Further accuracy tests on Adomian decomposition method for chaotic systems, Chaos, Solitons and Fractals, vol.36, issue.5, pp.1405-1411, 2008. ,
On accuracy of Adomian decomposition method for hyperchaotic Rössler system, Chaos, Solitons and Fractals, vol.40, issue.4, pp.1801-1807, 2009. ,
Numerical and physical modeling of the dynamics of the Lorenz system, Numerical Analysis and Applications, vol.7, issue.2, pp.159-167, 2014. ,
A new reliable numerical method for computing chaotic solutions of dynamical systems: the Chen attractor case, International Journal of Bifurcation and Chaos, vol.25, issue.13, p.1550187, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01323625
A new accurate numerical method of approximation of chaotic solutions of dynamical model equations with quadratic nonlinearities, Chaos, Solitons and Fractals, vol.91, pp.108-114, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01319597
On the reliability of computed chaotic solutions of non-linear differential equations, Tellus, vol.61, pp.550-564, 2009. ,
On the numerical simulation of propagation of micro-level inherent uncertainty for chaotic dynamic systems, Chaos, Solitons and Fractals, vol.47, pp.1-12, 2013. ,
On the mathematically reliable long-term simulation of chaotic solutions of Lorenz equation in the interval, Science China-Physics, vol.57, issue.2, pp.330-335, 2014. ,
Physical limit of prediction for chaotic motion of three-body problem, Communications in Nonlinear Science and Numerical Simulation, vol.19, pp.601-616, 2014. ,
On the inherent self-excited macroscopic randomness of chaotic three-body systems, International Journal of Bifurcation and Chaos, vol.29, issue.5, p.1530023, 2015. ,
On the clean numerical simulation (CNS) of chaotic dynamic systems, Journal of Hydrodynamics, vol.29, issue.5, pp.729-747, 2017. ,
, Phase transitions in tumor growth: III vascular and metastasis behavior, vol.462, pp.560-568, 2016.
Cryptanalysis of a classical chaos-based cryptosystem with some quantum cryptography features, International Journal of Bifurcation and Chaos, vol.27, issue.1, p.1750004, 2017. ,
Periodic flows to chaos based on discrete implicit mappings of continuous nonlinear systems, International Journal of Bifurcation and Chaos, vol.25, issue.3, p.1550044, 2015. ,
, Discretization and Implicit Mapping Dynamics, 2015.
Clean numerical simulation for some chaotic systems using the parallel multipleprecision Taylor scheme, Chinese Science Bulletin, vol.59, issue.33, pp.4465-4472, 2014. ,
Effective bounds for P-recursive sequences, Journal of Symbolic Computation, vol.45, issue.10, pp.1075-1096, 2010. ,
URL : https://hal.archives-ouvertes.fr/inria-00376219
A general method to derive Lyapunov functions for non-linear systems, International Journal of Control, vol.44, issue.2, pp.381-393, 1986. ,
Bounds for attractors and the existence of homoclinic orbits in the Lorenz system, Journal of Applied Mathematics and Mechanics, vol.65, issue.1, pp.19-32, 2001. ,
Bounds for a new chaotic system and its application in chaos synchronization, Communications in Nonlinear Science and Numerical Simulation, vol.16, issue.3, pp.1501-1508, 2011. ,
Estimating the bounds for the Lorenz family of chaotic systems, Chaos, Solitons and Fractals, vol.23, issue.2, pp.529-534, 2005. ,
Bounds of the hyper-chaotic Lorenz-Stenflo system, Communications in Nonlinear Science and Numerical Simulation, vol.15, issue.9, pp.2514-2520, 2010. ,
Ultimate bound estimation of a class of high dimensional quadratic autonomous dynamical systems, International Journal of Bifurcation and Chaos, vol.21, issue.9, p.2679, 2011. ,
, Recent new examples of hidden attractors, vol.224, pp.1469-1476, 2015.