1,211 research outputs found
Transition from homogeneous to inhomogeneous limit cycles : Effect of local filtering in coupled oscillators
10 pages, 8 FigsPeer reviewedPublisher PD
Chimeras in Leaky Integrate-and-Fire Neural Networks: Effects of Reflecting Connectivities
The effects of nonlocal and reflecting connectivity are investigated in
coupled Leaky Integrate-and-Fire (LIF) elements, which assimilate the exchange
of electrical signals between neurons. Earlier investigations have demonstrated
that non-local and hierarchical network connectivity often induces complex
synchronization patterns and chimera states in systems of coupled oscillators.
In the LIF system we show that if the elements are non-locally linked with
positive diffusive coupling in a ring architecture the system splits into a
number of alternating domains. Half of these domains contain elements, whose
potential stays near the threshold, while they are interrupted by active
domains, where the elements perform regular LIF oscillations. The active
domains move around the ring with constant velocity, depending on the system
parameters. The idea of introducing reflecting non-local coupling in LIF
networks originates from signal exchange between neurons residing in the two
hemispheres in the brain. We show evidence that this connectivity induces novel
complex spatial and temporal structures: for relatively extensive ranges of
parameter values the system splits in two coexisting domains, one domain where
all elements stay near-threshold and one where incoherent states develop with
multileveled mean phase velocity distribution.Comment: 12 pages, 12 figure
Synchronizability of chaotic logistic maps in delayed complex networks
We study a network of coupled logistic maps whose interactions occur with a
certain distribution of delay times. The local dynamics is chaotic in the
absence of coupling and thus the network is a paradigm of a complex system.
There are two regimes of synchronization, depending on the distribution of
delays: when the delays are sufficiently heterogeneous the network synchronizes
on a steady-state (that is unstable for the uncoupled maps); when the delays
are homogeneous, it synchronizes in a time-dependent state (that is either
periodic or chaotic). Using two global indicators we quantify the
synchronizability on the two regimes, focusing on the roles of the network
connectivity and the topology. The connectivity is measured in terms of the
average number of links per node, and we consider various topologies
(scale-free, small-world, star, and nearest-neighbor with and without a central
hub). With weak connectivity and weak coupling strength, the network displays
an irregular oscillatory dynamics that is largely independent of the topology
and of the delay distribution. With heterogeneous delays, we find a threshold
connectivity level below which the network does not synchronize, regardless of
the network size. This minimum average number of neighbors seems to be
independent of the delay distribution. We also analyze the effect of
self-feedback loops and find that they have an impact on the synchronizability
of small networks with large coupling strengths. The influence of feedback,
enhancing or degrading synchronization, depends on the topology and on the
distribution of delays.Comment: Submitted to "The European Physical Journal B" (EPJ B
Different Approaches of Synchronization in Chaotic-Coupled QD Lasers
The investigation of synchronization phenomena on measured theoretical data such as time series has recently become an increasing focus of interest. In this chapter, the synchronized states (including steady state, periodic or chaotic) in coupled quantum dot lasers (dimensionless rate equations) are considered with both bidirectional and unidirectional synchronization. Different approaches for measuring synchronization have been proposed that rely on certain characteristic features of the dynamical system under investigation. Results show that the measure to be applied to a certain task can be chosen according to information in test applications, although certain dynamical features of a system under investigation (e.g., bifurcation and amplitude correlation) may render certain measures more suitable than others
Neural Mechanisms Underlying the Generation of the Lobster Gastric Mill Motor Pattern
The lobster gastric mill central pattern generator (CPG) is located in the stomatogastric ganglion and consists of 11 neurons whose circuitry is well known. Because all of the neurons are identifiable and accessible, it can serve as a prime experimental model for analyzing how microcircuits generate multiphase oscillatory spatiotemporal patterns. The neurons that comprise the gastric mill CPG consist of one interneuron, five burster neurons and six tonically firing neurons. The single interneuron (Int 1) is shared by the medial tooth subcircuit (containing the AM, DG and GMs) and the lateral teeth subcircuit (LG, MG and LPGs). By surveying cell-to-cell connections and the cooperative dynamics of the neurons we find that the medial subcircuit is essentially a feed forward system of oscillators. The Int 1 neuron entrains the DG and AM cells by delayed excitation and this pair then periodically inhibits the tonically firing GMs causing them to burst. The lateral subcircuit consists of two negative feedback loops of reciprocal inhibition from Int 1 to the LG/MG pair and from the LG/MG to the LPGs. Following a fast inhibition from Int 1, the LG/MG neurons receive a slowly developing excitatory input similar to that which Int 1 puts onto DG/AM. Thus Int 1 plays a key role in synchronizing both subcircuits. This coordinating role is assisted by additional, weaker connections between the two subsets but those are not sufficient to synchronize them in the absence of Int 1. In addition to the experiments, we developed a conductance-based model of a slightly simplified gastric circuit. The mathematical model can reproduce the fundamental rhythm and many of the experimentally induced perturbations. Our findings shed light on the functional role of every cell and synapse in this small circuit providing a detailed understanding of the rhythm generation and pattern formation in the gastric mill network
Toward simple control for complex, autonomous robotic applications: combining discrete and rhythmic motor primitives
Vertebrates are able to quickly adapt to new environments in a very robust, seemingly effortless way. To explain both this adaptivity and robustness, a very promising perspective in neurosciences is the modular approach to movement generation: Movements results from combinations of a finite set of stable motor primitives organized at the spinal level. In this article we apply this concept of modular generation of movements to the control of robots with a high number of degrees of freedom, an issue that is challenging notably because planning complex, multidimensional trajectories in time-varying environments is a laborious and costly process. We thus propose to decrease the complexity of the planning phase through the use of a combination of discrete and rhythmic motor primitives, leading to the decoupling of the planning phase (i.e. the choice of behavior) and the actual trajectory generation. Such implementation eases the control of, and the switch between, different behaviors by reducing the dimensionality of the high-level commands. Moreover, since the motor primitives are generated by dynamical systems, the trajectories can be smoothly modulated, either by high-level commands to change the current behavior or by sensory feedback information to adapt to environmental constraints. In order to show the generality of our approach, we apply the framework to interactive drumming and infant crawling in a humanoid robot. These experiments illustrate the simplicity of the control architecture in terms of planning, the integration of different types of feedback (vision and contact) and the capacity of autonomously switching between different behaviors (crawling and simple reaching
Control of birhythmicity : A self-feedback approach
The authors thankfully acknowledge the insightful suggestions by the anonymous referees. DB acknowledges CSIR, New Delhi, India. TB acknowledges Science and Engineering Research Board (Department of Science and Technology, India) [Grant No. SB/FTP/PS-05/2013]. D.B. acknowledges Haradhan Kundu, Department of Mathematics, University of Burdwan, for his useful suggestions regarding computations.Peer reviewedPublisher PD
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