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**1 - 6**of**6**### Two-cluster bifurcations in systems of globally pulse-coupled oscillators

, 2013

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### Dynamics and Self-Organization,

, 2010

"... doi: 10.3389/fnsyn.2010.00032 Storage of phase-coded patterns via STDP in fully-connected and sparse network: a study of the network capacity ..."

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doi: 10.3389/fnsyn.2010.00032 Storage of phase-coded patterns via STDP in fully-connected and sparse network: a study of the network capacity

### Edited by:

, 2009

"... Large sparse circuits of spiking neurons exhibit a balanced state of highly irregular activity under a wide range of conditions. It occurs likewise in sparsely connected random networks that receive excitatory external inputs and recurrent inhibition as well as in networks with mixed recurrent inhib ..."

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Large sparse circuits of spiking neurons exhibit a balanced state of highly irregular activity under a wide range of conditions. It occurs likewise in sparsely connected random networks that receive excitatory external inputs and recurrent inhibition as well as in networks with mixed recurrent inhibition and excitation. Here we analytically investigate this irregular dynamics in finite networks keeping track of all individual spike times and the identities of individual neurons. For delayed, purely inhibitory interactions we show that the irregular dynamics is not chaotic but stable. Moreover, we demonstrate that after long transients the dynamics converges towards periodic orbits and that every generic periodic orbit of these dynamical systems is stable. We investigate the collective irregular dynamics upon increasing the time scale of synaptic responses and upon iteratively replacing inhibitory by excitatory interactions. Whereas for small and moderate time scales as well as for few excitatory interactions, the dynamics stays stable, there is a smooth transition to chaos if the synaptic response becomes sufficiently slow (even in purely inhibitory networks) or the number of excitatory interactions becomes too large. These results indicate that chaotic and stable dynamics are equally capable of generating the irregular neuronal activity. More generally, chaos apparently is not essential for generating the

### Complex Networks: A Review

"... In late 1950s, two mathematicians discovered a network with complex topology by random graph theory. Complex networks have received great attention in past few decades. Many studies have been done on complex networks and many are still in progress. Complex Networks are the networks which can be seen ..."

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In late 1950s, two mathematicians discovered a network with complex topology by random graph theory. Complex networks have received great attention in past few decades. Many studies have been done on complex networks and many are still in progress. Complex Networks are the networks which can be seen in real as well as in technological systems. They have nodes and these nodes are connected by various links. They are called complex networks because of the underlying complex architecture and complex topology. In this paper, our goal is to study the complex networks and various basic terms related to complex networks like mutual behavior between real-networks and complex networks, average path length, clustering coefficient, degree distribution. Designing and analyzing the behavior and dynamics of a complex networked system are also discussed. Hence, A complex networked system can helps us in: understanding the efficiency of new security approaches for computer networks, improving the design of computer networks to make it more robust and resilience against errors and failures occurred in system, understanding how population will respond to introduction of new nodes in system, detecting subtle vulnerabilities, and also detecting catastrophic failures in power grid. General Terms Understanding the complex networks, Study of complex networks

### Knowledge Management. Chapter in Knowledge Management Strategies for Business

, 2009

"... and Drive Innovation. In Knowledge management strategies: a handbook of applied ..."

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and Drive Innovation. In Knowledge management strategies: a handbook of applied