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A '''linear''' system is one whose response in a specified unit of measure, to a set of inputs considered at once, is the sum of its responses due to the inputs considered individually.
[[Linear algebra|Linear]] systems are easier to analyze mathematically and are a persuasive assumption in many models including the McCulloch and Pitts neuron, population coding models, and the simple neurons often used in [[Artificial neural network|artifical neural networks]]. Linearity may occur in the basic elements of a neural circuit such as the response of a postsynaptic neuron, or as an emergent property of a combination of nonlinear subcircuits.<ref name="MolnarHsueh2009">{{cite journal|last1=Molnar|first1=Alyosha|last2=Hsueh|first2=Hain-Ann|last3=Roska|first3=Botond|last4=Werblin|first4=Frank S.|title=Crossover inhibition in the retina: circuitry that compensates for nonlinear rectifying synaptic transmission|journal=Journal of Computational Neuroscience|volume=27|issue=3|year=2009|pages=569–590|issn=0929-5313|doi=10.1007/s10827-009-0170-6 | pmid = 19636690|pmc=2766457}}</ref> Though linearity is often seen as incorrect, there has been recent work suggesting it may, in fact, be biophysically plausible in some cases. <ref>{{Cite journal|last=Singh|first=Chandan|last2=Levy|first2=William B.|date=2017-07-13|title=A consensus layer V pyramidal neuron can sustain interpulse-interval coding|url=http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0180839|journal=PLOS ONE|volume=12|issue=7|pages=e0180839|doi=10.1371/journal.pone.0180839|issn=1932-6203}}</ref><ref>{{Cite journal|last=Cash|first=Sydney|last2=Yuste|first2=Rafael|date=1998-01-01|title=Input Summation by Cultured Pyramidal Neurons Is Linear and Position-Independent|url=http://www.jneurosci.org/content/18/1/10|journal=Journal of Neuroscience|language=en|volume=18|issue=1|pages=10–15|issn=0270-6474|pmid=9412481}}</ref>
==Examples==
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===NEURON===
The [[Neuron (software)|NEURON]] software, developed at Duke University, is a simulation environment for modeling individual neurons and networks of neurons.<ref>{{cite web|url=http://www.neuron.yale.edu/neuron/|title=NEURON - for empirically-based simulations of neurons and networks of neurons|publisher=}}</ref> The NEURON environment is a self-contained environment allowing interface through its [[Graphical user interface|GUI]] or via scripting with [[hoc (programming language)|hoc]] or [[Python (programming language)|python]]. The NEURON simulation engine is based on a Hodgkin–Huxley type model using a Borg–Graham formulation. Several examples of models written in NEURON are available from the online database ModelDB. <ref>McDougal RA, Morse TM, Carnevale T, Marenco L, Wang R, Migliore M, Miller PL, Shepherd GM, Hines ML.
Twenty years of ModelDB and beyond: building essential modeling tools for the future of neuroscience. J Comput Neurosci. 2017; 42(1):1-10.</ref>
==Embodiment in electronic hardware==
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