Pitchfork bifurcation and circuit implementation of a novel Chen hyper-chaotic system

Abstract

Dong En-Zeng( ) a)b) † , Chen Zeng-Qiang( ) a) , Chen Zai-Ping( ) b) , and Ni Jian-Yun( ) b)

Energy Conservation, Singular Orbits, and FPGA Implementation of Two New Hamiltonian Chaotic Systems

“…e complex dynamical behaviors of chaotic systems have been gradually excavated. Both conservative systems [4,5] and dissipative systems [6][7][8] have some phenomena of transition from period to quasi-period and then into chaos. For the past few years, due to the potential applications of chaotic systems with complex dynamic behavior in speech signals and digital image/video encryption, analysis in this area has also become one of the main directions of chaos research [9,10].…”

Local bifurcation analysis and ultimate bound of a novel 4D hyper-chaotic system

“…But it has not a unified and effective method to generate hyper-chaotic systems. By now, the usual technique to get a new 4D smooth quadratic autonomous hyper-chaotic system [4][5][6][7][8][9][10] is to add one more state variable to the three dimensional chaotic system, just as the Lorenz system [11], Chen system [12], Lü system [13], Qi system [14] and so on. There also some hyper-chaotic system is constructed directly [15][16][17][18], but this is difficult.…”

“…Pitchfork bifurcation of equilibrium positions is an important local static bifurcation and Hopf bifurcation is an important local dynamic bifurcation. The bifurcation point plays very important role in the studying of the stability of the equilibria [5,7,[19][20][21].…”

Synchronization of uncertain fractional-order chaotic systems with disturbance based on a fractional terminal sliding mode controller

“…Complex networks [3][4][5][6][7] are considered to be "between the rules and the random", [8] which is also the intrinsic character of chaotic dynamics, according to most physicists at present. Therefore, chaotic dynamics can be considered as a special kind of complex network with a wide range of potential applications, such as image encryption, [9,10] secure communication, [11,12] genetic networks, [13] and so on. Along with the development of chaos, fractional-order calculus has been used to describe the chaos system, and this extends the application field of chaos theory.…”