Awakened oscillations in coupled consumer-resource pairs

The paper concerns two interacting consumer-resource pairs based on chemostat-like equations under the assumption that the dynamics of the resource is considerably slower than that of the consumer. The presence of two different time scales enables to carry out a fairly complete analysis of the problem. This is done by treating consumers and resources in the coupled system as fast-scale and slow-scale variables respectively and subsequently considering developments in phase planes of these variables, fast and slow, as if they are independent. When uncoupled, each pair has unique asymptotically stable steady state and no self-sustained oscillatory behavior (although damped oscillations about the equilibrium are admitted). When the consumer-resource pairs are weakly coupled through direct reciprocal inhibition of consumers, the whole system exhibits self-sustained relaxation oscillations with a period that can be significantly longer than intrinsic relaxation time of either pair. It is shown that the model equations adequately describe locally linked consumer-resource systems of quite different nature: living populations under interspecific interference competition and lasers coupled via their cavity losses.Comment: 31 pages, 8 figures 2 tables, 48 reference

Clustered Chimera States in Systems of Type-I Excitability

Chimera is a fascinating phenomenon of coexisting synchronized and desynchronized behaviour that was discovered in networks of nonlocally coupled identical phase oscillators over ten years ago. Since then, chimeras were found in numerous theoretical and experimental studies and more recently in models of neuronal dynamics as well. In this work, we consider a generic model for a saddle-node bifurcation on a limit cycle representative for neural excitability type I. We obtain chimera states with multiple coherent regions (clustered chimeras/multi-chimeras) depending on the distance from the excitability threshold, the range of nonlocal coupling as well as the coupling strength. A detailed stability diagram for these chimera states as well as other interesting coexisting patterns like traveling waves are presented

Synchronization of globally coupled two-state stochastic oscillators with a state dependent refractory period

We present a model of identical coupled two-state stochastic units each of which in isolation is governed by a fixed refractory period. The nonlinear coupling between units directly affects the refractory period, which now depends on the global state of the system and can therefore itself become time dependent. At weak coupling the array settles into a quiescent stationary state. Increasing coupling strength leads to a saddle node bifurcation, beyond which the quiescent state coexists with a stable limit cycle of nonlinear coherent oscillations. We explicitly determine the critical coupling constant for this transition

A memristive non-smooth dynamical system with coexistence of bimodule periodic oscillation

© 2022 Elsevier GmbH. All rights reserved. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1016/j.aeue.2022.154279In order to explore the bursting oscillations and the formation mechanism of memristive non-smooth systems, a third-order memristor model and an external periodic excitation are introduced into a non-smooth dynamical system, and a novel 4D memristive non-smooth system with two-timescale is established. The system is divided into two different subsystems by a non-smooth interface, which can be used to simulate the scenario where a memristor encounters a non-smooth circuit in practical application circuits. Three different bursting patterns and bifurcation mechanisms are analyzed with the time series, the corresponding phase portraits, the equilibrium bifurcation diagrams, and the transformed phase portraits. It is pointed that not only the stability of the equilibrium trajectory but also the non-smooth interface may influence the bursting phenomenon, resulting in the sudden jumping of the trajectory and non-smooth bifurcation at the non-smooth interface. In particular, the coexistence of bimodule periodic oscillations at the non-smooth interface can be observed in this system. Finally, the correctness of the theoretical analysis is well verified by the numerical simulation and Multisim circuit simulation. This paper is of great significance for the future analysis and engineering application of the memristor in non-smooth circuits.Peer reviewe

High-feedback Operation of Power Electronic Converters

electronic

Observation of chaotic beats in a driven memristive Chua's circuit

In this paper, a time varying resistive circuit realising the action of an active three segment piecewise linear flux controlled memristor is proposed. Using this as the nonlinearity, a driven Chua's circuit is implemented. The phenomenon of chaotic beats in this circuit is observed for a suitable choice of parameters. The memristor acts as a chaotically time varying resistor (CTVR), switching between a less conductive OFF state and a more conductive ON state. This chaotic switching is governed by the dynamics of the driven Chua's circuit of which the memristor is an integral part. The occurrence of beats is essentially due to the interaction of the memristor aided self oscillations of the circuit and the external driving sinusoidal forcing. Upon slight tuning/detuning of the frequencies of the memristor switching and that of the external force, constructive and destructive interferences occur leading to revivals and collapses in amplitudes of the circuit variables, which we refer as chaotic beats. Numerical simulations and Multisim modelling as well as statistical analyses have been carried out to observe as well as to understand and verify the mechanism leading to chaotic beats.Comment: 30 pages, 16 figures; Submitted to IJB

Nonlinear resonance and excitability in interconnected systems

Engineering design amounts to develop components and interconnect them to obtain a desired behaviour. While in the context of equilibrium dynamics there is a well-developed theory that can account for robustness and optimality in this process, we still lack a corresponding methodology for nonequilibrium dynamics and in particular oscillatory behaviours. With the aim of fostering such a theory, this thesis studies two basic interconnections in the contexts of nonlinear resonance and excitability, two phenomena with the potential of encompassing a large number of applications. The first interconnection is considered in the context of vibration absorption. It corresponds to coupling two Duffing oscillators, the prototypical example of nonlinear resonator. Of primary interest is the frequency response of the system, which quantifies the behaviour in presence of harmonic forces. The analysis focuses on how isolated families of solutions appear and merge with a main one. Using singularity theory it is possible to organise these solutions in the space of parameters and delimit their presence through numerical methods. The second interconnection studied in this dissertation appears in the context of excitable circuits. Combining a fast excitable system and a slower oscillatory system that share a similar structure naturally leads to bursting. The resulting system has a slow-fast structure that can be leveraged in the analysis. The first step of this analysis is a novel slow-fast model of bistability between a rest state and a spiking attractor. Following this, the analysis moves to the complete interconnection, and in particular on how it can generate different patterns of bursting activity

Population-specific predictions for the finite Kuramoto model and collective synchronization in a system with resonant coupling

Synchronization of coupled simple harmonic oscillators is a well-studied problem in advanced undergraduate mechanics courses and the solution amounts to solving an eigenvalue problem. Synchronization of populations of auto-oscillators is a comparatively new field of study. The first scientists to consider such problems were mathematical biologists, but applied mathematicians and physicists have made significant contributions as well. The chief model of synchronization of distinct auto-oscillators is due to Kuramoto. The most striking feature of the model is the presence of a phase transition from an unsynchronized to a partially synchronized state at a critical value of the inter-oscillator coupling. Also, in spite of being a microscopic model that describes the interactions between individual oscillators, Kuramoto's model can be recast exactly as a mean field model. A great deal of work has focused on predicting the behavior of the mean field. The first part of this dissertation describes my work exploring the Kuramoto model. Most physicists have approached the problem by analyzing the behavior of infinitely sized systems. I focus instead on making precise predictions for specific, finitely sized populations of oscillators. In particular, I demonstrate that the assumption of a constant mean field leads to surprisingly good self-consistent predictions for the mean field, particularly if the frequency of synchronization is made a tunable parameter. However, I find that the discontinuities in the self-consistent predictions do not exhibit critical scaling, in contradiction with the known critical behavior exhibited by the Kuramoto model. The second part of this dissertation describes laboratory work and modeling of a mechanical system that exhibits synchronization. I examine the synchronization of 16 cell-phone vibrators coupled through a resonant plate. In light of the Kuramoto model, the interactions between the motors and the plate give somewhat unexpected results including bistability as well as ranges of frequencies in which the system never synchronize. I show, by starting with a first-principles model of the motors interacting with the plate, that the motors' interaction is similar to Kuramoto's model with two key differences: frequency-dependent coupling and a frequency-dependent phase delay