Abstract
A new class of 3D autonomous quadratic systems, the dynamics of which demonstrate a chaotic behavior, is found. This class is a generalization of the well-known class of Lorenz-like systems. The existence conditions of limit cycles in systems of the mentioned class are found. In addition, it is shown that, with the change of the appropriate parameters of systems of the indicated class, chaotic attractors different from the Lorenz attractor can be generated (these attractors are the result of the cascade of limit cycles bifurcations). Examples are given.
Highlights
Chaos is a very interesting nonlinear phenomenon, which has been intensively studied in the last four decades
Chaotic economic systems have got much attention because their complex dynamic behaviors cannot be described by traditional models
A new image encryption algorithm based on a chaotic economic map is proposed
Summary
Chaos is a very interesting nonlinear phenomenon, which has been intensively studied in the last four decades. System (1) is a three-dimensional autonomous system with only two quadratic terms in its nonlinearity, which is very simple in the algebraic structure and yet is fairly complex in dynamical behaviors The observation of these two seemingly contradictory aspects of the Lorenz system thereby triggered a great deal of interest from the scientific community to seek closely related Lorenz-like systems, by different motivations and from various perspectives [15]. It should be said (as it was noted in [15]) that almost all known chaotic attractors of 3D quadratic dynamical systems can be generated (at the appropriate values of parameters) by the following system:. In this work, the researches begun in [17, 18] will be continued
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