Analysis of a 3D chaotic system

By Gheorghe Tigan, Dumitru Opris. 2006

276 citations recorded by the source corpus.

A 3D nonlinear chaotic system, called the T system, is analyzed in this paper. Horseshoe chaos is investigated via the heteroclinic Shilnikov method constructing a heteroclinic connection between the saddle equilibrium points of the system. Partially numerical computations are carried out to support the analytical results.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fe59c80dfe30adf1653d4d9df4cdf81435ee5f85

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In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

Global Chaos Synchronization of Chemical Chaotic Reactors via Novel Sliding Mode Control Method (2015, background): “These classical chaotic systems paved the way to the discovery of many 3-D chaotic systems such as Arneodo system [5], Sprott systems [6], Chen system [7], Lü-Chen system [8], Cai system [9], Tigan system [10], etc.”
Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities (2014, methodology): “Some well-known 3-D chaotic systems are Arneodo system [45], Sprott systems [46], Chen system [47], Lü-Chen system [48], Liu system [49], Cai system [50], T-system [51], etc.”
A 3 - D Novel Conservative Chaotic System and its Generalized Projective Synchronization via Adaptive Control (2015, methodology): “This was followed by the discovery of many 3-D chaotic systems in the chaos literature such as Rössler system [3], Rabinovich system [4], ACT system [5], Sprott systems [6], Chen system [7], Lü system [8], Shaw system [9], Feeny system [10], Shimizu system [11], Liu-Chen system [12], Cai system [13]”
Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates (2014, background): “The transition rate between S (Susceptible) and I (infected) is β I, where β is the contact rate, which takes into account the probability of getting the disease in a contact between a susceptible and an infectious subject [5–8].”
Adaptive Chaotic Synchronization of Enzymes-Substrates System with Ferroelectric Behaviour in Brain Waves (2015, background): “The discovery of Lorenz and Rössler chaotic systems has ben followed by the discovery of many 3-D chaotic systems such as Arneodo system [5], Sprott systems [6], Chen system [7], Lü-Chen system [8], Cai system [9], Tigan system [10], etc.”