Analytical and numerical investigation of a new Lorenz-like chaotic attractor with compound structures

Hyperchaos in a Conservative System with Nonhyperbolic Fixed Points

“…, and the subscript "AP" denotes the acceleration of these state variables at any point. Through the comparison of (17) and (18), it is found that the solutions to (17) must be the solutions to (18), but there may exist other solutions to (18). PPs are these points where all the acceleration of these state variables of the system (16) is zero but the velocities are not [36], which can be denoted by…”

“…So far, chaos theory has been successfully applied in many fields, such as electronic engineering [4], computer science [5], communication systems [6,7], complex networks [8], chemical engineering [9], and economic models [10]. In the recent decade, hundreds of physical chaotic models [11][12][13][14] and artificial chaotic systems [15][16][17][18][19] have been investigated in theory and by numerical simulations due to the potential applications of chaotic system in various chaos-based technologies [20,21]. By now, numerous dissipative-chaosbased encryption algorithms have been developed to ensure the safety of information, but these algorithms are not strong enough because the dissipative chaotic attractors can be reconstructed by delay embedding method based on the sampled data.…”

On new chaotic and hyperchaotic systems: A literature survey

“…For example, when (a, b, c, k) = (4, 10, 5, 0), system (26) can generate three coexisting chaotic attractors whose Lyapunov exponents are equal to 0.699, 0.457 and 0.520. Also, this system is characterized by a variable equilibriums number by varying the parameter c. If c < 16bk 2 /(4ab + 1) 2 , system (26) has three equilibriums. If c = 16bk 2 /(4ab + 1) 2 , it has four equilibriums and if c > 16bk 2 /(4ab+1) 2 , it has five equilibriums.…”

“…In 2013, Jia and Wang discovered a novel class of hyperchaotic systems [22]. This class is obtained by adding a state feedback to system (2). It is written aṡ…”

A New No-Equilibrium Chaotic System and Its Topological Horseshoe Chaos

“…Since Lorenz found an atmosphere dynamical model which can generate butterfly-shaped chaotic attractor in 1963 [1], chaos theory in the past five decades has attracted a lot of attention and hence triggered the emergence of a huge literature in this area. Since then, many kinds of chaotic or hyperchaotic systems governed by nonlinear ordinary differential equations (ODEs), including autonomous and nonautonomous chaotic systems [2][3][4], continuous and discrete chaotic systems [5][6][7], integer-order and fractionalorder chaotic systems [1,2,7,8], and chaotic systems with self-excited attractor and hidden attractor [9][10][11], were developed, and continuous chaotic systems governed by nonlinear partial differential equations (PDEs) [12][13][14] were also investigated.…”