A parameter space method for analyzing Hopf bifurcation of fractional-order nonlinear systems with multiple-parameter

An explicit Hopf bifurcation criterion of fractional-order systems with order 1 < α < 2

“…To demonstrate the effectiveness of our explicit method in the multi-parameter situation, we use the same system analyzed by the online method [9]. Consider the fractional-order neural network system with multiple parameter as follows:…”

“…For example, in the problem of Hopf bifurcation about fractional-order neural network systems, several neuron parameters are set to a same bifurcation parameter or the sum of some parameters is set to a single bifurcation parameter [5,6], although the fact is that different neuron parameters have different values 10 [7,8]. For high-dimensional fractional-order systems with multi-parameter, an online method [9] is suitable to determine the Hopf bifurcation hyper-surface through a visual representation of the parameter space if the systems have fewer parameters. However, the online method may fail because of the computational complexity of multi-parameter.…”

Order-dependent sampling control of uncertain fractional-order neural networks system

“…It is well known that stability is the most important issue in control systems, and it is the first condition for the system to work properly. For FO systems, there are a number of interesting results in the analysis of stability in the sense of Lyapunov, including asymptotic stability [20], uniform stability [21], stability [22], Hopf bifurcation analysis [23,24] and Mittage-Leffler stability [18,19]. The robustness and performance analysis of FO systems have attracted the attention of many scholars, especially for FONNs systems with uncertainty.…”

“…When the controller gain matrix K is unknown, it is evident that the (23) isn't an LMI because some crosses of these determined parameters are described in (23) in a nonlinear fashion P K. However, it can be transformed into an LMI by the following Corollary 2. Corollary 2.…”

Order-dependent sampling control of uncertain fractional-order neural networks system

“…It is well known that stability is the most important issue in control systems, and it is the first condition for the system to work properly. For FO systems, numerous interesting conclusions have been obtained in the literature of proving system stability by Lyapunov function, containing asymptotic stability [20], consistent stability [21], stability [22], Hopf-Bifurcation research [23,24], Mittage-Leffler stability [18,19]. At present, the research has attracted more and more researchers' attention on the robustness and performance for FO systems, specially for FONN systems with uncertainties.…”