Analytical and numerical study of nonlinear dynamics of a ﬁnance system
In this paper, a mathematical model of a nonlinear ﬁnance chaotic system showing complicated regular and chaotic behaviors is investigated. Based on the Lyapunov function, deﬁnitions of globally exponentially attractive set and positive invariant are introduced. Theorems on the existence of the globally exponentially attractive set and positive invariant, of periodic solutions, of Poincare—Andronov—Hopf bifurcation existence and theorems in the ﬁeld of control of attractors are formulated and proved. Based on complex numerical investigation, for the ﬁrst time for this system one has built a map of dynamic regimes depending on the bifurcation parameter and one has found all the major transition scenarios to deterministic chaos.