We describe the dynamics of learning in unsupervised linear feature-discovery networks that have recurrent lateral connections. Bifurcation theory provides a description of the location of multiple equilibria and limit cycles in the weight-space dynamics.

The self-organization of recurrent feature-discovery networks is studied from the perspective of dynamical systems. Bifurcation theory reveals parameter regimes in which multiple equilibria or limit cycles coexist with the equilibrium at which the networks perform principal component analysis.

Abstract Dynamical properties of limit cycles for a tropically discretized negative feedback model are numerically investigated. This has controlling parameter τ, which corresponds to time interval the evolution phase in cycles. By considering τ as bifurcation parameter, we find that ultradiscrete state emerges due lock caused by saddle-node bifurcation. Furthermore, focusing on max-plus model,...

An autonomous free-running Ćuk converter is studied in this paper. Analysis of the describing nonlinear state equations shows that the system loses stability via a supercritical Hopf bifurcation. The boundary of stability is derived and local trajectories of motion studied. Cycle-by-cycle simulations of the actual system reveal the typical bifurcation from a stable equilibrium state to chaos, v...

Abstract. In this paper, dynamical complexities of a three species food chain model with Holling type IV predator response is investigated analytically as well as numerically. The local and global stability analysis is carried out. The persistence criterion of the food chain model is obtained. Numerical bifurcation analysis reveals the chaotic behavior in a narrow region of the bifurcation para...