Robustness and Stability of Limit Cycles in a Class of Planar Dynamical Systems

Using the Andronov-Hopf bifurcation theorem and the Poincaré-Bendixson Theorem, this paper explores robust cyclical possibilities in a generalized Kolmogorov-Lotka-Volterra class of models with positive intraspecific cooperation in the prey population. This additional feedback effect introduces nonlinearities which modify the cyclical outcomes of the model. Using an economic example, the paper proposes an algorithm to symbolically construct the topological normal form of Andronov-Hopf bifurcation. In case the limit cycle turns out to be unstable, the possibilities of the dynamics converging to another limit cycle is explored

Convergence, cycles and complex dynamics of financing investment

This paper demonstrates the diverse dynamical possibilities of a simple macroeconomic model of debt-financed investment-led growth in the presence of interest rate rules. We show possibilities of convergence to steady state, growth cycles around it as well as various complex dynamics from codim 1 and codim 2 bifurcations. The effectiveness of monetary policy in the form of interest rate rules is examined under this context

Convergence, cycles and complex dynamics of financing investment

This paper demonstrates the diverse dynamical possibilities of a simple macroeconomic model of debt-financed investment-led growth in the presence of interest rate rules. We show possibilities of convergence to steady state, growth cycles around it as well as various complex dynamics from codim 1 and codim 2 bifurcations. The effectiveness of monetary policy in the form of interest rate rules is examined under this context

Macrodynamics of debt-financed investment-led growth with interest rate rules

This paper demonstrates the diverse dynamical possibilities arising out of a simple macroeconomic model of debt-financed investment-led growth in the presence of interest rate rules. We show possibilities of convergence to steady state, growth cycles around it as well as various complex dynamics. We investigate whether, given this framework, the financial sector can provide endogenous bounds to an otherwise unstable system. The effectiveness of monetary policy in the form of a Taylor-type interest rate rule targeting capacity utilization is examined under this context

Macrodynamics of debt-financed investment-led growth with interest rate rules

This paper demonstrates the diverse dynamical possibilities arising out of a simple macroeconomic model of debt-financed investment-led growth in the presence of interest rate rules. We show possibilities of convergence to steady state, growth cycles around it as well as various complex dynamics. We investigate whether, given this framework, the financial sector can provide endogenous bounds to an otherwise unstable system. The effectiveness of monetary policy in the form of a Taylor-type interest rate rule targeting capacity utilization is examined under this context