Fig 1.
Plot of Lyapunov exponents for system (2) for initial conditions [0.1, 0.01, 0.01], when a = 0.8, b = 0, c = 0.01, d = −7.4, r = 6 and l = −2.
Fig 2.
Plot of Lyapunov exponents for system (2) for initial conditions [0.1, 0.01, 0.01], when a = 0.3, b = 0.2, c = 0.3, d = −7.4, r = 6 and l = −2.
Fig 3.
Plot of Lyapunov exponents for system (2) for initial conditions [0.1, −0.03, −0.06], when a = 0.05, b = 0.04, c = −0.03, d = −4, r = 4 and l = −5.
Fig 4.
Plot of Bifurcation diagram for system (2) for initial conditions [0.1, 0.01, 0.01], when b ∈ [0, 0.5] a = 0.8, c = 0.01, d = −7.4, r = 6 and l = −2.
Fig 5.
Plot of Bifurcation diagram for system (2) for initial conditions [0.1, 0.01, 0.01], when b ∈ [0.2, 0.3760] a = 0.3, c = 0.3, d = −7.4, r = 6 and l = −2.
Fig 6.
Plot of Bifurcation diagram for system (2) for initial conditions [0.1, −0.03, −0.06], when b ∈ [0.04, 0.3560] a = 0.05, c = −0.03, d = −4, r = 4 and l = −5.
Table 1.
A comparison of Lyapunov exponents and Kaplan-Yorke dimension of three recently reported 3-D chaotic systems (2).
Fig 7.
Poincaré section.
Fig 8.
Local phase portraits of system (2) is a hidden attractor for initial conditions [0.1, 0.01, 0.01], when a = 0.8, b = 0, c = 0.01, d = −7.4, r = 6 and l = −2: On the x, y, and z planes, there is a 3D projection.
Fig 9.
Local phase portraits of system (2) is a hidden attractor for initial conditions [0.1, 0.01, 0.01], when a = 0.8, b = 0, c = 0.01, d = −7.4, r = 6 and l = −2: On the x, and y planes, there is a 2D projection.
Fig 10.
Local phase portraits of system (2) is a hidden attractor for initial conditions [0.1, 0.01, 0.01], when a = 0.8, b = 0, c = 0.01, d = −7.4, r = 6 and l = −2: On the y, and z planes, there is a 2D projection.
Fig 11.
Local phase portraits of system (2) is a hidden attractor for initial conditions [0.1, 0.01, 0.01], when a = 0.8, b = 0, c = 0.01, d = −7.4, r = 6 and l = −2: On the x, and z planes, there is a 2D projection.
Fig 12.
Poincaré section.
Fig 13.
Local phase portraits of system (2) is a self-excited attractor for initial conditions [0.1, 0.01, 0.01], when a = 0.3, b = 0.2, c = 0.3, d = −7.4, r = 6 and l = −2: On the x, y, and z planes, there is a 3D projection.
Fig 14.
Local phase portraits of system (2) is a self-excited attractor for initial conditions [0.1, 0.01, 0.01], when a = 0.3, b = 0.2, c = 0.3, d = −7.4, r = 6 and l = −2: On the x, and y planes, there is a 2D projection.
Fig 15.
Local phase portraits of system (2) is a self-excited attractor for initial conditions [0.1, 0.01, 0.01], when a = 0.3, b = 0.2, c = 0.3, d = −7.4, r = 6 and l = −2: On the y, and z planes, there is a 2D projection.
Fig 16.
Local phase portraits of system (2) is a self-excited attractor for initial conditions [0.1, 0.01, 0.01], when a = 0.3, b = 0.2, c = 0.3, d = −7.4, r = 6 and l = −2: On the x, and z planes, there is a 2D projection.
Fig 17.
Poincaré section.
Fig 18.
Local phase portraits of system (2) is a self-excited attractor for initial conditions [0.1, −0.03, −0.06], when a = 0.05, b = 0.04, c = −0.03, d = −4, r = 4 and l = −5: On the x, y, and z planes, there is a 3D projection.
Fig 19.
Local phase portraits of system (2) is a self-excited attractor for initial conditions [0.1, −0.03, −0.06], when a = 0.05, b = 0.04, c = −0.03, d = −4, r = 4 and l = −5: On the x, and y planes, there is a 2D projection.
Fig 20.
Local phase portraits of system (2) is a self-excited attractor for initial conditions [0.1, −0.03, −0.06], when a = 0.05, b = 0.04, c = −0.03, d = −4, r = 4 and l = −5: On the y, and z planes, there is a 2D projection.
Fig 21.
Local phase portraits of system (2) is a self-excited attractor for initial conditions [0.1, −0.03, −0.06], when a = 0.05, b = 0.04, c = −0.03, d = −4, r = 4 and l = −5: On the x, and z planes, there is a 2D projection.
Fig 22.
Poincaré section.
Fig 23.
Local phase portraits of system (2) is periodic for initial conditions [0.005, 0.055, 0.005], when a = 1.7088, b = 5, c = 2, d = −7, r = 4 and l = −1: On the x, y, and z planes, there is a 3D projection.