Potential Function in a Continuous Dissipative Chaotic System: Decomposition Scheme and Role of Strange Attractor

Lyapunov function as potential function: A dynamical equivalence

“…[35] We also show that potential functions can be constructed in continuous dissipative chaotic systems and can be used to explain for the different origins of chaotic attractor and strange attractor. [41] 4. Discussion…”

Dynamics of rotator chain with dissipative boundary

“…Heat baths turn the equations of motion of the system from odinary differential equations to stochastic differential equations. Recent developments on stochastic process reveals that there are correspondences between the deterministic dynamics of a system and its stochastic counterpart when a specific stochastic interpretation other than Itô and Stratonovich is used [17][18][19]. As a result, it is reasonable to investigate the transport properties of rotator chain by calculating the steady state distribution of the model based on the dynamics of its deterministic counterpart.…”

“…For the total energy E of the system dE ds = 0, the work done by driving torque must be balanced by the dissipation at both end τ ω = 2αω 2 , combined with (10) we conclude that at spiral all rotators have same angular momenta ω = τ /2α. Substituting this result and ( 17) into (19) leads to the relation j = τ 2 /4α. The proof provides a strong evidence that the monotonically increasing segment represent the globally synchronous rotation state of rotator chain.…”