Revisiting linear augmentation for stabilizing stationary solutions: potential pitfalls and their application

Abstract

Linear augmentation has recently been shown to be effective in targeting desired stationary solutions, suppressing bistablity, in regulating the dynamics of drive response systems and in controlling the dynamics of hidden attractors. The simplicity of the procedure is the highlight of this scheme but at the same time questions related to its general applicability still need to be addressed. Focusing on the issue of targeting stationary solutions, this work demonstrates instances where the scheme fails to stabilize the required solutions and leads to other complicated dynamical scenarios. Appropriate examples from conservative as well as dissipative systems are presented in this regard and potential applications for relevant observations in dissipative predator--prey systems are also discussed.

updated version with title change, additional figures, text and explanations

References in corpus (5)

• Distributed Delays Facilitate Amplitude Death of Coupled Oscillators
• Extreme events in excitable systems and mechanisms of their generation
• Route to extreme events in excitable systems
• Noise-induced cooperative dynamics and its control in coupled neuron models
• Collective Atomic Recoil Laser as a synchronization transition

Cited by in corpus (1)

• Revival of oscillation from mean-field-induced death: Theory and experiment